Linking two and three
In thisIn this chachapterpter
8A Painting and wallpapering
8B Tiling, carpeting and
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290 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
With the shell of their home completed, Jaclyn and Kim now have to consider the
This chapter deals with:
1. ﬁnishing the internal walls
2. ﬁnishing the ﬂoors
3. planning the kitchen
1 Draw nets for the following 3-D ﬁgures.
a b c
2 Calculate the outer surface area of the following ﬁgures.
3 The sketch below shows a shed with a gable roof.
a Draw a plan of the walls of the shed. Label your diagram with measurements.
b Calculate the area of the walls.
c Sketch the shape of the roof, labelling your diagram with dimensions.
d Calculate the surface area of the roof.
e Calculate the height of the roof above the walls.
f Determine the pitch of the roof.
g Draw a ﬂoor plan of the shed.
h Sketch the northern elevation of the shed.
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4 The following diagram represents the ﬂoor plan of a kitchen. The bench/cupboard
width around the perimeter is 590 mm.
a Calculate the total ﬂoor area of the kitchen.
b Determine the exposed ﬂoor area.
5 In landscaping his back yard, Jim removed soil to install a circular in-ground swim-
ming pool with a 10-m radius and a depth of 1.5 m.
a Calculate the volume of soil that Jim would need to remove.
b If the soil that was removed to install the pool was used to top-dress the lawn, what
would be the depth of the top-dressing?
Finishing the walls
Two wall ﬁnishes commonly used today are
paint and wallpaper.
When painting walls and ceilings, it is necessary
to know the following information:
1. area to be painted
2. number of coats of paint to be applied
3. coverage of the paint (number of square
metres covered by 1 litre of the paint)
4. size and cost of the paint containers.
Jaclyn would like to paint all the ceilings of
their Sturt home white. She prefers different
pastel colours on the walls of each room.
This is obviously more expensive than painting
all the walls the same colour.
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292 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
If we were to calculate the cost of paint for a room of a house, we would need to
make allowances for windows, doors and other openings. To calculate the areas of
these, we would need measurements. Some plans indicate measurements of all features
in great detail. In this case, it is a simple process to read dimensions from the plan, and
use these ﬁgures in calculations.
Since the ﬂoor plan of the Sturt design does not indicate detailed measurements, or
even a scale, it would ﬁrst be necessary to determine the scale. (It is assumed that the
diagram is drawn to scale.) Combining ruler measurements with the scale would then
produce the actual dimensions of openings.
The ceiling of the whole Sturt design (including the verandah) is to be painted white. The
paint covers 12 m2
per litre and can be purchased in 6-litre tins at $43.50 per tin. Two
coats of paint are required. Use the ﬂoor plan of the Sturt design to calculate the cost of
paint for the job.
Draw a diagram using the ﬂoor plan.
Determine the dimensions of the ceiling
Calculate the area of the ceiling. Ceiling is 16 m × 8.925 m
Area of ceiling = 16 m × 8.925 m
= 142.8 m2
Determine the quantity of paint
required (remember, 2 coats).
No. of litres of paint required
= 142.8 ÷ 12 × 2 litres
= 11.9 × 2 litres
= 23.8 litres
Find the number of tins required (round
up if necessary).
No. of tins of paint = 23.8 ÷ 6
= 3.97 tins
So 4 tins of paint are needed.
Determine the cost of paint. Cost of paint = $43.50 × 4
So the paint for the job would cost $174.
1 16 000 = 16 m
= 8.925 m
From a printout of the ﬂoor plan of the Sturt design shown on the CD, determine:
a the scale of the plan
b the width of the door and window in bedroom 3.
a Measure the length of one side of the
house with a ruler, and compare this with
the measurement indicated on the plan.
a 231 mm as measured with a ruler on the
plan represents 16 000 mm on the house,
that is 231 mm : 16 000 mm
Convert this to a scale. So the scale is 1 : 69
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Once the dimensions of the openings are known, the area to be painted can be calcu-
lated by subtracting the area of the openings from the total area of the walls. It must be
recognised that, if details are not supplied, and we are required to measure from a plan,
these measurements are subject to slight errors. Answers obtained using this technique
will be estimates.
b Measure door and window widths with
b The door measures 12 mm
The window measures 26 mm
Use the scale to determine actual
The house measurements are 69 times the
∴ Door width = 12 mm × 69
= 828 mm
Window width = 26 mm × 69
= 1794 mm
The walls of bedroom 3, including the wardrobe doors, are to be painted light blue. The
entry door and windows are both 2040 mm high, while the ceiling is 2400 mm high. A
white undercoat (ﬁrst coat) is applied, then a ﬁnal coat of light blue. Both the blue and the
white paint come in 2-litre tins at a cost of $21.50 per tin. Coverage of the paint is
/L. What would be the cost of the paint for bedroom 3?
Continued over page
Draw a plan of the walls opened out
Calculate the total area of walls. Total area of walls = 12 m × 2.4 m
= 28.8 m2
Determine the areas of the sections
which are not to be painted (use scale
and ruler measurements from the
previous worked example).
Area of window = 1.794 m × 2.04 m
= 3.66 m2
Area of door = 0.828 m × 2.04 m
= 1.69 m2
Calculate the painted area. Area to be painted
= total area walls − (area window + area door)
= 28.8 − (3.66 + 1.69) m2
= 28.8 − 5.35 m2
= 23.45 m2
Find the quantity of paint required for
No. of litres of paint required per coat
= 23.45 ÷ 14 L
= 1.675 L
3 m 3 m 3 m
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294 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
An alternative to painting the walls of a building is wallpapering. This is a job many
people ﬁnd they are capable of doing themselves. Standard wallpaper rolls are 10 m
long and 50 cm wide. The wallpaper is applied in drops (strips) from the top of the
wall. If the paper displays a pattern, allowances must be made to match adjacent drops.
When estimating the number of rolls of paper required for a job, it is normal practice
not to make allowance for windows or doors (unless, of course, these areas are large).
It is also not possible to purchase part of a roll. Since the most common ceiling height
these days is 2400 mm, this ﬁgure will be assumed unless otherwise stated.
Calculate the no. of tins required for each
colour (round up if necessary).
No. of tins for each coat
= 1.675 ÷ 2 tins
= 0.8375 tins
So 1 tin is required for each coat.
Determine the total cost of paint. Cost of 1 tin of white + 1 tin of blue
= $21.50 × 2
How many rolls of wallpaper would be required to wallpaper the three walls of bedroom 1
in the Sturt design, if each roll is 50 cm wide and 10 m long? (Do not make allowance for
any openings, and assume that the paper does not require pattern matching.)
Draw the plan of the walls out ﬂat,
Determine the total length of the walls
to be papered.
Total length of walls to be papered
= 4.1 m + 3.5 m + 4.1 m
= 11.7 m
Calculate the number of drops of
wallpaper required (remember to
convert to the same units ﬁrst).
No. of drops required = 11.7 m ÷ 50 cm
= 11.7 m ÷ 0.5 m
Round up the number of drops if it is
not a whole number.
So 24 drops would be required
Calculate the total length of drops (each
drop is 2.4 m long).
Each drop is 2.4 m long
∴ Length of 24 drops = 24 × 2.4 m
= 57.6 m
Find the number of rolls (each roll
10 m long).
No. of rolls = 57.6 m ÷ 10 m
Round up the number of rolls if it is not
a whole number.
∴ It would required 6 rolls of wallpaper to
cover the 3 walls of bedroom 1.
3.5 m 4.1 m
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The aim of this investigation is to
determine the effect of a pattern
on applying wallpaper.
1 On a sheet of plain A4 paper, draw
up a grid of 1-cm squares.
2 Cut this sheet into 2-cm-wide strips
down its length.
3 Tape the ends of the strips, making
sure that the pattern is continued
correctly, to form one continuous
length. Roll this length of paper to
form your wallpaper roll.
4 Take another sheet of A4 paper.
Its measurements are approximately
21 cm wide and 29.6 cm long.
This piece of paper will represent
the wall to be covered with your
5 With your sheet of paper in the portrait position (the direction you usually place
paper for writing), cut strips from your roll of paper to wallpaper your wall,
remembering to match the pattern of grids.
6 Did you need to waste wallpaper at the ends and beginnings of drops? What
was the situation with your last drop? What would be the effect of large
patterns in wallpapers?
7 Write up this investigation under the headings:
a aim of investigation
d conclusion/s and recommendation/s.
1. When estimating the cost of paint required for a job, we need to know the area
to be painted, the number of coats required, the paint coverage, and the sizes
and cost of the paint tins.
2. When detailed measurements are not indicated, estimates are obtained from the
plan using the scale.
3. Remember to make allowances for openings when estimating painting areas.
4. Wallpaper comes in rolls 10 m long and 50 cm wide. Determine the length of
wall to be papered, making no allowance for openings, unless they are large.
5. For painting and wallpapering, assume a ceiling height of 2400 mm, unless
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296 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
Painting and wallpapering
1 A 10-m by 15-m recreation hall needs its ceiling painted with two coats of white
paint. The paint covers 12 m2
/L and can be bought in 4-litre tins at $36 per tin.
Complete the following to calculate the cost of paint for the job.
a Label the measurements of the ceiling on a diagram.
b Area of ceiling =
c No. of litres of paint required for two coats =
d No. of tins of paint =
e Cost of paint =
2 If the paint in question 1 was supplied in 3-litre tins for $27 per tin (the same price
per litre), what would be the cost of the paint?
3 The front elevation of a garage shows a roller door measuring 5 cm square on the
plan. If the scale of the plan is 1:50, how many litres of paint would be required to
give the roller door 3 coats, if the paint coverage is 14 m2
4 A bedroom, 3.8 metres square, has built-in wardrobes from ﬂoor to ceiling completely
down one wall. The exterior wall has a window 1000 mm by 900 mm. Calculate the
number of tins of paint required for two coats of the walls (excluding wardrobes and
the window) if the paint can be purchased only in 2-litre tins and the paint has a
coverage of 12 m2
/L. (Assume a ceiling height of 2400 mm.)
5 A church hall is 50 m by 20 m. Uniformly positioned on both sides down the length
of the hall are 6 stained glass windows each measuring 0.5 m by 2 m. The ceiling is
3 m high. The walls need to be coated with a varnish covering 10 m2
/L. How much
varnish would be required for two coats?
6 A rumpus room has the dimensions shown.
a Determine the number of litres of each type of
paint required for the walls using a white undercoat
which covers 12 m2
/L and two coats of full gloss
blue enamel paint with a coverage of 18 m2
b How much paint would be required for the ceiling with a white undercoat
/L coverage) and two coats of white matt acrylic paint (16 m2
c The prices of the various types of paint are:
undercoat $6.50 per litre
full gloss enamel $14.45 per litre
acrylic $9.95 per litre.
Calculate the cost of painting the rumpus room if the paint can be purchased only
in 2-litre tins.
7 Wallpaper can be purchased in rolls 50 cm wide and 10 m long. Ignoring openings in
the room, complete the following to determine the number of rolls of wallpaper required
to cover the walls of a room that is 3.5 m square, and which has a ceiling 2.4 m high.
a Label the net with wall widths and height.
b Length of wall to be papered =
c No. of drops of wallpaper =
d Length of each drop =
e Total length of all the drops =
f No. of rolls required =
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8 If the walls of the rumpus room in question 6 were to be wallpapered instead of
painted, how many rolls of wallpaper 50 cm wide and 10 m long would be required?
9 Sandra and Nick want to compare the cost of wallpapering their games room with the
cost of painting. The costs are as follows.
1. Wallpaper costs $22.50 for a roll which is 50 cm wide and 10 m long.
2. Undercoat (1 coat) covers 12 m2
/L and costs $6.50 per litre. (This is available in
3. Semi-gloss acrylic (2 coats required) covers 18 m2
/L and costs $14 per litre (avail-
able in 1-litre tins).
If their games room is 12 m long and 6 m wide, and has 2.4-m ceilings, advise the
cost to wallpaper and to paint (ignore openings).
10 A standard wallpaper roll costs $22.50. Low sheen acrylic paint is available for
$11.50 per litre. It covers 16 m2
/L. Two coats are required. On a square-metre basis, is
it cheaper to wallpaper or paint?
Finishing the ﬂoors
If a building is erected from a concrete slab on the ground, the slab (that is, the ﬂoor of
the building) is frequently covered with tiles or carpet. In the upper levels of structures,
where the ﬂoor is not a concrete slab, polished timber is sometimes selected.
When tiles are laid on a ﬂoor, they are glued in place, then a grout mixture is rubbed
between the tiles, similar to the way in which mortar is used to bind bricks together.
View the Construction section of the CD which demonstrates tiling in action.
Many tiling patterns are quite intricate, sometimes depicting several
geometric shapes. Often, tiles are cut and placed at various angles.
To calculate the number of tiles required for a job is often
complex. For this reason, any tiling problems in this
text will quote a price which represents an average
price per square metre of tiles laid with
grout. Any calculated cost for a job will
represent an estimate, because of
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298 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
Sometimes, a tiling estimate is required from a ﬂoor plan which does not indicate detailed
measurements. It is then necessary to use the plan scale ﬁrst, to determine dimensions.
Estimate the cost of covering the ﬂoor below with tiles at
a price of $42.50/m2
Calculate the area of the ﬂoor as a
composite area of 2 rectangles.
Area of ﬂoor = area of 2 rectangles
= (10 m × 8 m) + (4 m × 7 m)
= 80 m2
+ 28 m2
= 108 m2
Find the total cost, given the price per
Cost of tiling = $42.50 × 108
A kitchen plan has an island bench in the centre.
Give an estimate for tiling the ﬂoor at a cost of
for laid tiles.
Use the plan scale to determine the
Scale is 1 : 100
So actual measurements are 100 times plan
Length of room = 4 cm × 100
= 400 cm
= 4 m
Width of room = 2.5 m
Island bench is 2 m by 1 m
No tiling is required under the island
bench. The area to be tiled is the area of
the island bench subtracted from the
area of the room.
Area of room = 4 m × 2.5 m
= 10 m2
Area of island bench = 2 m × 1 m
= 2 m2
So area to be tiled
= area of room − area island bench
= 10 m2
− 2 m2
= 8 m2
Calculate the cost of tiling. Cost of tiling = $45 × 8
Scale 1 : 100
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Another popular ﬂoor covering is carpet. This comes
in rolls, and is purchased by the linear metre. (It is not
necessary to buy the whole roll as it is with wallpaper.)
The carpet is generally laid in parallel strips. Because
the width of a room is often not an exact multiple of the
carpet width, there is wastage from the side of the last
carpet strip laid (as with wallpapering). These offcuts are
sometimes bound around the edges and used as scatter rugs.
If a carpet depicts a pattern which requires matching
of strips, this also contributes to wastage. In our
carpeting calculations, we will assume no pattern
matching (unless otherwise stated), and that the carpet
is laid in strips parallel to the longest wall.
Carpet can be purchased in rolls 3.66 metres wide at a cost
of $75 per linear metre. What would be the cost of purchasing
carpet for the ﬂoor shown in the diagram?
Draw the room, showing all
Lay strips 3.66 m wide parallel to the
Lay the carpet in strips parallel to the 12-m
Determine whether strips all need to be
the same length.
Two 12-m-long strips cover a width of 7.32 m
(with some cut off at the edge of the 2nd strip).
One 8-m-long strip covers to a width of
10.98 m (so some is cut off the side).
Find the total length of all strips. So the total length of the carpet
= two 12-m lengths + one 8-m length
= 32 m
Calculate the cost. Cost of carpet = $75 × 32
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300 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
The aim of this investigation is to determine whether the length of carpet required
for a room depends on the direction of laying.
1 We’ll initially start with carpet that ﬁts neatly when laid in either direction.
a Cut a piece of paper into strips that are 2 cm wide, tape the strips together,
then roll them up to simulate a carpet roll.
b On a sheet of paper, draw the outline of a rectangle 8 cm by 6 cm. This
represents the ﬂoor to be carpeted.
c Taking your paper roll, lay strips in the rectangle, parallel to the longer side
(the 8-cm one), cutting the strips to the required length.
d How many strips did you need? What total length of the roll was required?
e Repeat your experiment, laying your strips of paper parallel to the 6-cm
side. How many strips did you need? What total length of the roll was
f What do you conclude from the above?
2 Repeat the experiment with a rectangle 9 cm by 7 cm. What do you conclude?
3 Repeat again with a rectangle 7 cm by 6 cm. Note your conclusion.
4 Assume you work for a carpet ﬁrm, and your boss has asked you to investigate
this matter. Write a report, detailing your ﬁndings.
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How you lay out your kitchen can have a great impact on how effectively you can work
in it, and consequently, whether you enjoy or dread preparing meals in it.
Planning the kitchen
The ﬂoor plan of the Sturt design shows the kitchen as viewed from above. It indicates
bench space with a sink and hotplates. Adjacent to the sink is a pantry, and space
for a refrigerator is directly opposite.The plan does not show the types of ﬂoor cabinet
and drawers beneath the bench, nor does it show any overhead wall cabinets.
The design and relative position of items in the kitchen are very important
considerations, as a great deal of time is generally spent in food preparation. In
order to make informed decisions in planning a kitchen, it is necessary to consider
the following facts.
1. The three major items used in the kitchen are the sink, hotplates/oven, and
refrigerator. These should be arranged in what is called the work triangle.
2. Between these three items there should be sufﬁcient bench space to allow for
food preparation and cleaning up afterwards.
3. A set-down space of at least 450 mm should be provided beside the refrigerator
and hotplates/oven for safety as well as convenience.
4. The oven and/or microwave can be built into a wall cabinet.
5. It is best not to break up bench space by placing items in the middle of it.
Your task is to place ﬂoor and wall cabinets in the kitchen of the Sturt design.
Proceed as follows.
1 Choose from the range of kitchen cabinets (A to U) shown in 3-D format and
top-view format on the following pages. Remember to consider the
measurements carefully so cabinets ﬁt in the available spaces.
2 Assume that the kitchen bench is 875 mm high.
3 On a sheet of graph paper, rule up a scale as indicated on the kitchen planner
(shown on page 304).
4 Draw a ﬂoor plan of the kitchen on graph paper, marking the relative positions
of the cabinets that you have chosen from the A to U list.
5 On graph paper, draw elevations of the three walls of the kitchen, showing all
ﬂoor and wall cabinets.
This type of kitchen is known as a U-shaped kitchen. It is generally considered to
be the most workable kitchen shape. Other kitchen shapes are:
1. L-shaped kitchens
These are generally situated in a long, narrow room where the kitchen
cupboards and major appliances lie along two adjacent walls.
1. Corridor kitchens
As the name implies, these kitchens are narrow rooms with cupboards placed
on two opposite walls, leaving a passageway between them.
2. Galley kitchens
These are one-wall kitchens, usually found in dwellings where space is limited
(home units, studios).
Investigate the G.J. Gardner CD and plans in newspapers or brochures to locate
kitchens of the types described above.
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302 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
(Source: Olympic Laminates Pty Ltd.)
C. Wall Corner
K. Oven cabinet
J. 2 Drawers 600
I. 2 Drawers plus
1 deep drawer 600
H. 4 Drawer 600
G. 4 Drawer 450
(top quality metal
T. Pantry cabinet 400
U. Pantry cabinet 800
P. Elevated range
(with black top
front rail. Available
in all models. Use 3
range doors 400)
O.Deep corner floor cabinet 900
Narrow corner floor cabinet 750
S. Deep pantry terminal
shelf (available in
R. Deep floor terminal shelf
(available in limited styles)
Q. Wall terminal shelf
F. Microwave oven cabinet
E. Preparation cabinet
(bench and wall mounted)
Note: Glass doors are
available for 400mm and
800mm wall units in limited
styles. Wall cabinets measure
315mm front to back
Deep floor cabinets
measure 590mm from
front to back, including
the door. Narrow floor
440mm from front to
back including the door.
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Copy and use these models to plan your kitchen layout
WALL CABINETS FLOOR CABINETS
A. Single door wall cabinet G. 4 Drawer cabinets 450
Two door floor cabinet 900
N. Three door floor cabinet 1200
H. I. J. Drawer cabinets 600
4 Drawer 3 Drawer 2 Drawer
B. Two door wall cabinets
K. Oven cabinet
L. Single door floor
L. FLOOR CABINET
Single door floor
ELEVATED RANGE CABINET
P. Elevated range cabinet 1200
Two door floor cabinet 800
M. Two door floor cabinet 600
Single door floor
C. Wall corner cabinets
D. Range cabinets
E. Preparation cabinet
E. Microwave oven cabinet
Note: BREAKFAST BAR:
Can be any number of floor units with 820mm deep bar top. (It is best to continue off a corner unit.) If you are using more than
1 individual unit in your plan copy extra shapes. All dimensions quoted are nominal and include the thickness of the door.
Source: Olympic Laminates Pty Ltd.
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304 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
1 m 2 m 3 m 4 m
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Tiling, carpeting and kitchen
1 Calculate the cost of laying tiles on the
ﬂoor shown in this plan if tiles cost $45/m2
2 The bathroom shown in the plan contains a shower
and a vanity basin.
a Determine the cost of tiling the ﬂoor at $42/m2
b Two walls of the shower are to be tiled to a
height of 1.8 m. What would this cost using tiles
priced at $38/m2
3 A conference room measures 12 m by 6 m. Carpet is sold by the linear metre from rolls
that are 3.66 m wide. Draw diagrams for each of the following situations and determine
the length of carpet required to cover the ﬂoor if the carpet is laid:
a parallel to the longer side.
b parallel to the shorter side.
4 It was decided to put a border of 30-cm-square tiles around the perimeter of the confer-
ence room in question 3 and to carpet the remainder of the ﬂoor in the centre.
a Draw a diagram showing measurements and features on the ﬂoor.
b Determine the number of tiles around the perimeter of the room.
c Find the length of carpet required if it was laid parallel to the longer side.
d How many linear metres of carpet would be needed if it was laid parallel to the
1. When tiling a ﬂoor, determine the area to be tiled, taking into account those
areas covered by other ﬁxed objects.
2. Tiling costs are quoted by the square metre.
3. Carpet is manufactured in rolls and purchased by the linear metre.
4. The carpet is laid in strips parallel to the longest side of a room. With non-
rectangular rooms, the carpet strips may be of different lengths. Draw a
diagram to conﬁrm lengths of all strips.
5. Kitchen cabinets and drawers are available in a variety of sizes. Floor cabinets
are generally 875 mm high and 590 mm deep.
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306 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
5 A room is 14.2 m square. It can be tiled at a cost of $36/m2
. In order to carpet the room
for the same outlay, what priced carpet could be used? (Carpet can be bought by the
metre from rolls that are 3.66 m wide.)
6 Refer to the kitchen cabinet plans on pages 302 and 303.
a Wall cabinets come in various sizes.
i What is the maximum height of the wall cabinets?
ii Give the size of a microwave oven cabinet.
iii A corner cabinet would take up how much space?
b Refer to the ﬂoor cabinets displayed.
i What are the dimensions of the oven cabinet?
ii Give the most common height of a ﬂoor cabinet.
iii What options are available for a corner ﬂoor cabinet?
iv What choice is there in the ‘non-corner’ pantry cabinet range?
c What ﬂoor area does the ‘Two-door ﬂoor cabinet 600’ occupy?
d What depth are the ﬂoor cabinets?
e How deep are the majority of the wall cabinets?
7 A kitchen measures 3.2 m by 3.6 m.
a Draw a scale ﬂoor plan of the kitchen.
b Two adjacent walls must be outﬁtted with a ﬂoor cabinet with drawers, an oven
cabinet, a corner cabinet, a pantry cabinet and ﬂoor cabinets with shelving. Design
a kitchen using the range of furniture on pages 302 and 303. Make sure that the
dimensions of the furniture can be accommodated by the size of the kitchen. Pre-
pare a scale drawing of your plan.
8 The two-door wall cabinet B (900 mm long) is available in pine timber. To seal the sur-
face of the wood, it can be varnished. Ignore the thickness of the timber in the
following calculations and do not round ﬁgures.
a Calculate the total surface area of the doors, inside and outside.
b Determine the area of the 4 exterior surfaces of the cabinet. (Ignore the surface
which is attached to the wall.)
c Calculate the surface area of the shelf (top and bottom).
d Find the area of the 5 internal surfaces of the cabinet.
e What is the total area of the exposed surfaces of the cabinet?
f If the varnish covers 10 m2
/L and the cabinet requires 2 coats, how much varnish
would the job require (to the nearest mL)?
9 The preparation cabinet houses electrical appliances (mixer, toaster, etc.) on the base
and smaller utensils on the three shelves above. If the tallest electrical appliance is
40 cm, draw a plan of the cabinet showing the position of the three shelves. Justify their
placement with an explanation.
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C h a p t e r 8 C o n s t r u c t i o n : T h e ﬁ n i s h i n g t o u c h e s 307
The scale diagram below is a site plan for a block of land on which a house is to be
1 Calculate the dimensions of the block of land.
2 How long is the perimeter of the block?
3 Concrete costs $130/m3
. If the driveway is laid with concrete 5 cm thick, what would
be the cost of concrete for the job?
4 Calculate the dimensions of the house.
5 What is the ﬂoor area of the house in square metres?
6 If the house faces the same direction as the garage, in which direction does the back
of the house face?
7 Carpet can be purchased in rolls 3.66 m wide. If the carpet strips are laid parallel to
the longer side of the house, how many metres of carpet would be required to cover
the ﬂoor of the house? (Ignore the internal walls of the house.)
8 If the carpet was laid parallel to the shorter side of the house, what length of carpet
would be required?
9 If the swimming pool is 1.5 m deep, what is its capacity in kL?
10 Give an estimate of the number of square metres of turf required to lay grass around
the pool inside the fenced area.
Scale 1 cm ⇔ 4 m
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308 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
With the house ﬁnishing touches almost completed, it is now time for Jaclyn and Kim
to turn their attention to landscaping. Let’s begin by accessing this option on the CD.
In order to cost accessories that provide comfort in our daily lives, we must apply
some of the mathematical techniques that were considered in the previous chapter.
We’ll consider several landscaping applications by investigating some practical situ-
ations. The selection includes:
1. landscaping a garden bed
2. building a gate and fence
3. designing a sprinkler system
5. preparing a quote for a simple shed.
1 Choose the Sturt design from the CD and place it on the land. The size of the
block available is 40 m by 40 m. The block size for this investigation is 30 m
by 30 m. With the drawing option, construct a fence around the boundary. This
will help with the relative placement of items on the land. It can be removed
later, if necessary.
2 The house does not necessarily have to be positioned parallel to the road. Enter
the option ‘Layout tips’ and decide the best direction for the house. Use the
move/rotate/mirror options to achieve the optimum position.
3 This particular house design does not incorporate a garage. Position a carport/
garage on the land where you would consider it to be most convenient.
4 Use the drawing tool to provide a driveway to the garage and a path to the front
5 Position the clothes hoist, and draw a path leading to it.
6 Draw any other options you would like to include (tennis court, swimming
pool), then landscape with trees, remembering that they provide shade, but also
7 Use the measuring tool to determine the distance of the external walls of the
house from the boundaries.
8 Measure the dimensions of the house with the measuring tool. Calculate the
percentage of the land covered by the house.
9 Add any ﬁnishing touches, then print out your landscaped design.
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C h a p t e r 8 C o n s t r u c t i o n : T h e ﬁ n i s h i n g t o u c h e s 309
Landscaping a garden bed
In this activity we consider the construction of a 10-metre-square garden, raised
above the ground, with treated pine as a border.
1 Draw a plan of the garden.
1. There are two options for the border:
(a) treated pine sleepers (200 mm wide, 75 mm deep) are sold in 2.4-metre
(b) treated pine pole (100 mm wide, 75 mm deep) comes in 1.8-metre
2. The sleepers are twice as wide as the poles.
3. Our garden bed is to be 400 mm high.
2 Draw two front elevations of the bed detailing the number of lengths of each
type of pine required for the structure. (Remember, they come in different
3. Compare the cost of constructing the garden bed using sleepers with the cost of
a pine pole structure. Which would you recommend?
4. Determine the cost of ﬁlling the garden bed with soil at $30/m3
5. What would be the total cost of the project?
Treated Pine Pole FROM
• 75 x 100 x 1.8 m. $5.25 PLM.
• 125 x 150 x 1.8 m. $10.15 PLM
• 200 x 75 mm
x 2.4 m
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310 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
Building a gate and fence
Consider the gate shown in the illustration above. Construct a model as follows.
1 Cut 0.5-cm strips of paper to use for the pickets, the frame and the bracing.
2 Using 9 pickets as shown, assemble these evenly over a frame that consists of
two vertical and three horizontal rails (adjust your frame, if necessary, to
accommodate your pickets).
3 Provide a bracing strip between the two horizontal rails.
4 Assuming that the gate is 1 m wide, determine the scale of your model.
5 Measure the total length of your pickets. Using your scale factor, and the prices
above, calculate the cost of the pickets required.
6 Similarly, determine the cost of the frame and bracing using treated pine fence
7 What is the total cost of the gate?
Use a similar process to design a section of the fence illustrated above using treated
pine fence palings and treated pine fence posts and rails. Decide on a height for the
fence. Use the prices given to determine a cost per metre for the fence.
Wet Rough Sawn Treated Pine FROM
• 75 x 38 mm. $1.70 PLM
• 75 x 50 mm. $2.20 PLM
Treated Pine Fence Palings • 150 mm x 1.8 m. $1.65 FROM
Treated Pine Fence Plinth • 150 x 25 mm. $1.75 PLM Treated Pine Fence Post H4
• 100 x 100 mm. $6.20 PLM Treated Pine Fence Rails • 75 x 38 mm. $1.70 PLM
• 100 x 38 mm. $2.20 PLM • 75 x 50 mm. $2.20 plm • 100 x 50 mm. $2.95 PLM
Treated Pine Windsor Pickets FROM
• 0.9 m. $1.35 • 1.2 m. $1.75
• 1.5 m. $2.25 • 1.8 m. $2.75
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C h a p t e r 8 C o n s t r u c t i o n : T h e ﬁ n i s h i n g t o u c h e s 311
A sprinkler system
Underground sprinkler systems are commonplace in suburban homes. In this
investigation, we consider decisions that must be made to achieve a system which
adequately fulﬁls the job of watering the required area.
For this activity we have access to sprinklers that can spray areas of the
1. full circle
2. half circle
3. quarter circle
1 Let’s consider the placement of sprinklers
in the rectangular lawn shown at right.
a What problems do you notice?
b What percentage of the lawn does it water?
c What would be the length of underground
piping necessary for the system?
d Would it make a difference to the length of
piping necessary if it was laid width-ways rather than length-ways?
2 You will have noticed areas of the lawn in the above diagram that do not
receive water spray.
a Investigate a placement for the sprinklers which would provide a 100%
coverage of the lawn. (Draw a scale diagram using a compass.)
b What length of underground piping would be required in this case?
3 Some above-ground sprinklers
provide circular patterns; others
oscillate and spray in an
approximately rectangular pattern.
Investigate a design for an
underground system using rectangular
pattern sprinklers. Would it provide
more efﬁcient lawn coverage?
Two booklets available free in
gardening stores provide a guide to
watering. Produced by Pope, they are
called Easy Guide to Installing Lawn
Pop-up Systems and Easy Guide to
When Should I Water. Sections of the
former booklet are reproduced here.
Study the printed material, then try to
devise a system which would be
appropriate for an area in your school
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312 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
The Pope Rating Points used in the example above are the recommended values
for the ‘Professional 50 mm Spray Pop-Up’ shown in the illustration directly
below. For areas where the water ﬂow is low, the ‘Low Pressure Spray Pop-Up’ is
recommended, with Pope Rating Points as indicated in the illustration at the
bottom of the page.
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Anyone contemplating the installation of an underground sprinkler system should
take time to plan the position and types of Spray Pop-Ups carefully. A planning
grid is provided on the following page.
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314 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
Soil types and watering
On the following page is an extract from a pamphlet produced by Pope entitled,
Easy Guide to When Should I Water.
Study the information carefully, then answer the questions:
1. How frequently should you water during hot weather if your soil is clay?
2. Why should clay soil generally require watering less frequently than sandy
3. Why is it beneﬁcial to water in the evening?
4. How would you adjust the watering recommendations if you lived in Tasmania?
5. What is the beneﬁt of aerating lawns in spring?
6. If using a professional 50-mm spray pop-up on loam, what is the recommended
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C h a p t e r 8 C o n s t r u c t i o n : T h e ﬁ n i s h i n g t o u c h e s 315
7. Overall, the professional 50-mm spray pop-up requires less watering than the
other sprinkler systems. Which units are next on the list in terms of low
8. How high should couch grass be cut in winter?
9. Why should the cool season grasses be cut higher?
Find out the soil types where you live and at your school. Write a recommendation
for care of the lawn and garden at each place.
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316 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
It is quite common these days to air-condition part or all of a private dwelling. Air-
conditioning single rooms requires a system which is usually built into the wall. For
larger areas, units are built into the roof or an exterior wall. Some systems offer
reverse cycle air-conditioning (these units provide cool air in summer and warm air
in winter). Ducting to the rooms is usually provided between the ceiling and the roof.
1 Visit a store to obtain information on air-conditioning.
2 What types of units are available?
3 Investigate the ducting system required.
4 What costs are involved in purchasing various units?
5 What costs are incurred in installing the various types of unit?
6 What are the running costs in terms of electricity usage?
Split Ducted Air Conditioner
Above the ceiling or below the floor you won’t see it but you’ll
feel the difference
• Air can be delivered to an outlet in any room or area
• The air flow rate to each outlet can be individually controlled
• Zone control allows sleeping areas at night or living areas
during the day to be conditioned separately
• Air outlets positioned throughout the conditioned space
provide positive air distribution with the elimination of ‘dead’
spots, air short cycling or draughts
• No noise indoors, ultra quiet outdoors
• No need for large, unsightly fascia units
• No need to put large holes in the walls or damage the building
• No costly maintenance is necessary, just regular cleaning of
the air filter by the owner
• Hidden insulated ducting to each outlet minimises heat losses
• Easy to use finger tip control of temperature and fan speed
• Year round operation with cost efficient heating in Winter and
cooling in Summer
• The split system design allows for optimum positioning of the
outdoor condensing unit
A comprehensive range of models, with both cooling
only and reverse cycle operation, is available from
7.0 kW to 18.0 kW output capacities
• Pressed, heavy gauge, metal outdoor cabinet.
Enamel painted fro long life protection
• Dynamically balanced aerofoil fan and motor
assemblies for low noise and vibration free
• 350 mm low profile indoor fan coil unit for easier
• Room thermostat with on/off, heat/cool and fan
• 3 speed, high static pressure, indoor fan to suit
long duct runs
• Electrical, pressure and thermal safety controls
• High efficiency lanced aluminium fin and copper
tube heat exchangers
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Preparing a quote for a simple shed
In this investigation we consider the quantities and types of material required
for the construction of a simple shed. Once these have been determined, a
quote for the supply of the goods can be prepared. This is an open-ended
activity, allowing for ﬂexibility of design and choice of construction materials.
Prices quoted for materials represent an ‘average’ cost with respect to the range
1 Draw a rough sketch of a simple garden shed that would suit your needs.
2 Decide on measurements that would be suitable. These include:
a size of slab (which is 100 mm thick)
b dimensions of footings (consult the ‘Footings and slabs’ section in the
previous chapter for suitable measurements)
c height of walls (for a shed these need not be 2400 mm)
d style and pitch of roof.
3 Prepare scale drawings of:
a ﬂoor plan
b all elevations.
4 Using cardboard, construct a simple model of your shed.
The slab and footings
5 Calculate the volume of concrete required for the footings and slab.
6 If concrete costs $130/m3
, determine the cost for this part of the job.
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318 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
7 The walls may be constructed from a
timber frame covered with a suitable
cladding. Framing costs approximately
. Choose a cladding from one
illustrated on the next page. Determine
the length of weatherboard required,
then calculate the cost.
Another alternative is colorbond
sheet metal cladding. Colorbond costs
A brick wall would cost approximately $55/m2
Concrete tiles cost $35/m2
Colorbond metal sheets are $12/m2
Preparing the quote
8 Design a quote form detailing information such as:
a cost of footings and slab
b cost of walls
c cost of roof.
9 Calculate the cost per square metre for your shed.
To keep the above calculations simple, we have ignored factors such as roof
trusses, windows and doors. In reality, you could take your design to a building
supplier who would use a computer program to determine the quantities of all
materials that you would need. Frames and roof trusses could be assembled off site
for you, other materials could be cut to size and the shed could be delivered to you
in a ‘pre-fabricated’ state ready for you to assemble.
Hardies Newport Hardies Summit
• 4200 x 170 mm
$1565 • 4200 x 230 mm
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Questions 1–4 use information found in the investigation on landscaping a garden bed
(see page 309). Bob is planning the construction of a retaining wall 7.2 m long and 1 m
high. He can use treated pine sleepers or treated pine poles (which come in two sizes).
1 Imagine that you are planning a retaining wall constructed of treated pine sleepers.
a What is the length of a sleeper?
b How many sleepers would be required per row?
c What is the width of a sleeper?
d How many rows of sleepers would be required?
e What number of sleepers would be needed for the wall?
f What is the cost of one sleeper?
g What would be the cost of the sleepers for the wall?
2 Now imagine that you are planning the retaining wall constructed of treated pine poles
(75 mm × 100 mm × 1.8 m). Answer each part in question 1 above, for treated pine
poles of this size.
3 Repeat question 1 using treated pine poles 125 mm × 150 mm × 1.8 m as the building
4 Write a paragraph comparing the merits of the three types of timber which could be
used to construct the retaining wall.
Question 5 requires information that can be located in the investigation on building a
gate and fence (see page 310).
5 a The wet rough sawn treated pine is available in two sizes.
i Explain what the following measurements represent.
75 × 38 mm
75 × 50 mm
ii Which size is better value?
iii If 5 boards of each type were stacked ﬂat on top of each other in two piles, what
would be the difference in height of the two stacks?
iv If you ordered the same length of the two boards and the difference in cost was
$5, what length of each type did you order?
b Treated pine fence rails are available in 4 sizes:
i Which are the widest?
ii Which are the thinnest?
iii What are the smallest and largest cross-sectional areas?
iv Of the two rails that cost the same per linear metre, which size is better value for
1. Landscaping often requires planning, using scale drawings.
2. Most frequently, landscaping requirements are an application of geometry
techniques and the mathematics of money.
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320 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
6 Refer to the investigation on sprinklers (pages 311 to 314) for information relating to
a According to the graph on page 312, if it took 25 seconds to ﬁll a 9-litre bucket
from a tap turned on full, what would be the tap’s rating?
b Give two combinations of professional 50-mm spray pop-ups that would be suitable
for the tap.
c Give two combinations of low pressure spray pop-ups that would be suitable for
d If four quarter-sprinklers, each with a stream throw of 3 metres, were used to water
a lawn that is 6 metres square, draw a design showing the optimum position of the
sprinklers. Calculate the percentage of the lawn receiving direct water from the
7 This garden shed is 2.5 m wide, 1.5 m deep and 2 m high. It has colorbond walls and
door, with a colorbond gable roof at a pitch angle of 20°. It is erected on a concrete slab
100 mm thick with footings 200 mm wide and 200 mm deep around the perimeter.
a Calculate the volume of concrete in the footings.
b Determine the volume of concrete required for the slab.
c If concrete costs $130/m3
, what is the cost of concrete for the job?
d Calculate the area of colorbond in the walls and door.
e Using the pitch angle of the roof, calculate the perpendicular height of the tri-
angular gable section. Hence determine the total area of these sections, front and
f Use the pitch angle to determine the dimensions of the roof. Hence calculate the
g Determine the total area of colorbond.
h Calculate the cost of the metal sheeting at $12/m2
i What is the total cost of materials for the shed?
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C h a p t e r 8 C o n s t r u c t i o n : T h e ﬁ n i s h i n g t o u c h e s 321
• The quantity of paint required for a job depends on the area to be painted, the paint
coverage and the number of coats. Allowance is made for openings.
• Wallpaper is hung vertically in drops, and is purchased by the roll. In estimating the
number of rolls required, no allowance is made for openings.
• The quantity of tiles necessary for a job depends on the area being tiled.
• Carpet is laid in strips, generally parallel to the longest side of the room.
Furnishing a kitchen
• Kitchen cabinets and drawers come in a variety of sizes.
• Careful planning using scale drawings leads to a kitchen design that is practical and
• Landscaping provides pleasurable surroundings. Lawns, gardens, fences and sheds
contribute to the overall comfort of the occupants.
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322 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
1 A lounge room is 5.4 m by 4.2 m with a ceiling that is 2.4 m high. The window in the exterior
wall measures 1.5 m by 1 m.
a Calculate the cost of painting the ceiling with 2 coats of white acrylic (coverage 16 m2
b The elevation of the plan shows the exterior windows of the lounge room having
measurements of 6 cm and 4 cm. What is the scale of the plan?
c What would be the cost of painting the walls of the lounge with 2 coats of semi-gloss
acrylic (coverage 18 m2
/L) if the paint can be purchased in 1-litre tins at $14 per tin?
d Determine the cost of wallpapering the lounge at $21/roll. Wallpaper rolls are 50 cm wide
and 10 m long (ignore openings).
2 An entertainment room with a view towards the mountains
has dimensions as shown:
a Calculate the area of the room.
b What would be the cost to tile the whole ﬂoor at $38/m2
for laid tiles?
c If the centre rectangular section was carpeted and the triangular
sections on the edges were tiled:
i how much would the tiles for these sections cost?
ii what would the carpet cost at $85/m2
? (Carpet rolls are 3.66 m wide.) Indicate whether
there is a difference in cost depending on the direction in which the carpet is laid.
8B 5 m
5 m 5 m
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3 Consider the design of a kitchen.
a What is meant by the ‘work triangle’?
b What alternatives are available in wall cabinets to provide wall storage down the entire
length of a 3.4-m wall?
c What volume does the wall corner cabinet occupy?
d If the non-corner pantry cabinets are arranged with the shelves evenly spaced, what is the
distance between the shelves?
4 A plant nursery constructed a raised rectangular garden bed using treated pine sleepers to
retain the soil. The bed, measuring 24 m by 12 m, was two sleepers high around the
perimeter. (See page 309 for sleeper sizes and costs.)
a How many sleepers would be required?
b Calculate the cost of the sleepers.
c If the bed was ﬁlled to within 20 cm of the top of the border, how much soil would be
d What would be the soil cost at $30/m3
5 An animal enclosure was built using treated pine fence palings. The enclosure was 1.8 m
high, surrounding an area 30 m by 15 m. (See page 310 for paling sizes and costs.)
a How many palings would be required for the whole enclosure?
b What would be the cost of the palings?
c What area would it enclose?
d If the enclosure had been 25 m by 18 m it would have provided the same area. Would the
same number of palings be required? How many?
e An enclosure 20 m by 22.5 m also provides the same area. How many palings would be
required in this instance?
f What can you deduce about the number of palings required and the shape of the
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324 M a t h s Q u e s t M a t h s A Ye a r 1 1 f o r Q u e e n s l a n d
6 Refer to the investigation on soil types and watering (pages 314 and 315) for information
relating to this question.
a Which type of soil (sand, loam or clay) provides the greatest drainage? Which provides
b Other than for the sake of appearance, why should weeds be removed from a garden?
c Why is it not advisable to spread too much fertiliser on lawns?
d Explain the recommendation, ‘Thin/scarify your lawn in spring for healthy lawns and
e Name a warm climate grass. Generally these grasses have a broader leaf than the cool
climate grasses. What advantage is this?
f Clay soil requires watering less frequently but for a longer period of time than sandy soil.
g Of the Original Series Sprinklers, the Capitol Sprinkler requires less watering time than
the other two. Why would you then choose one of the other two?
h Why is it inadvisable to sprinkle for extended periods of time?
7 A garden tidy is constructed of durable metal in the shape of a rectangular prism with a lid.
With dimensions 1510 mm by 750 mm and a height of 1000 mm, it offers protection against
the weather for the storage of outdoor items. To protect against vermin, the structure stands on
a concrete slab 100 mm thick.
a Calculate the volume of concrete in the slab.
b What would be the cost of the concrete at $130/m3
c Determine the area of metal required for the structure.
d At $15/m2
, what would be the cost of the metal?
e If you were constructing this garden tidy in your back yard, what could you expect to pay
f What volume would the tidy store?
g If the structure was used for storing wood, what would be the longest length that could be
stored in the tidy?
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