Unit Conversion: General Mathematics

2. In
pairs,
†hink of †he †ype of volume
questions

3. 10 cm
8 cm

4. :8c
m
Worki
n
Triangle Area
=
= 6 x 8=
48 m2
Rectangle = Ix b
= 6 x 12 =
72cm
Total Area = 72 + 42
8
= 120 m
Volume = Area x length
= 120 x 15
=1800*,3

5. :8c
m
Worki
n
Triangle Area
=
= 6 x 8=
48 m2
Rectangle = Ix b
= 6 x 12 =
72cm
Total Area = 72 + 42
8
= 120 m
Volume = Area x length
= 120 x 15
=1800*,3

6. :8c
m
Worki
n
Triangle Area
=
= 6 x 8=
48 m2
Rectangle = Ix b
= 6 x 12 =
72cm
Total Area = 72 + 42
8
= 120 m
Volume = Area x length
= 120 x 15
=1800*,3

8. 3. A tin of tuna is in the shape of a cylinder.
10 cm
It has diameter 10 centimetres and height 4 centimetres.
Calculate its volume.
Take n = 3•14.
4 cm

9. 4
cm
1(i cm

10. J inn keeps his ironing in a storage box is hich has a volume half that of the
basket.
35 cm
28 cm
The storage box is in the shape of
a cuboid, 35 centimetres 25 centimetres
broad.
(b) f”ind the height of the storage box.
long and
[X100/203] Page three (Turn o

12. In
pairs,
†hink of †he †ype of volume
questions

16. www.ma†
hsrevision.com
N5 LS
r = rodius
=
Perpendiculor
heigh†
Volume Cone
=
Voiume
Cone

17. 3. The diagram shows a cone.
1O«m
The height is 1 2 centimetres and the radius of the base 10 centimetres.
Calculate the volume of the cone.
Take a = 3•14.

19. In
pairs,
†hink of †he †ype of volume
questions

20. 2
.
Success Criterio
To kno *he volume
formuo forvorous
bos shopes
WorkoutvoIumeSfo
r compos{e
shapes.
Ans wer to contoin
appropr idt e units and
wo rk ng.

21. WWW.
a
†
hsrevision.com
NS
LS
Voium
e
Sphere
r = radiU5 =
2°
D = diameter
Voiume
Q. If the above sphere has radius
10cm.
Calculate it's volume.
3
Volume = 4
n(1O)3
=4187cm3
†o 4 sig.
figs)

22. The diagram below represents a sphere.
6c
m
The sphere has a diameter of 6
centimetres. Calculate its volume.
Take a 3-14.

24. In
pairs,
†hink of †he †ype of volume
questions

25. 2
.
Success Criterio
To kno *he volume
formuo forvorous
bos shopes
WorkoutvoIumeSfo
r compos{e
shapes.
Ans wer to contoin
appropr idt e units and
wo rk ng.

26. * Volume - Cylinder + half a
sphereCylinde
r
spher
e

28. '. (n) A cylindrical paperweight of radius 3
centimetres and height 4 centimetres is filled with sand.
Calculate the volume of sand in the paperweight.
Par† b on next slide

29. 9. Perfecto Ice C ream is sold in cones and cylindrical tubs with measurements as
shown bclou'
20 cm
I
cm
Both the cone and the tub of ice cream cost the same.
Which container of ice cream is better value for mone;'?
Give a reason for your answer.
5.8
cm

30. 3. A concrete block is in the shape of a prism.
22
cm
60 cm
22 cm
32 cm
32 cm
The cross section of the prism is a trapezium with dimensions as shown.
(o) Calculate the area of the cross section.
(6) Calculate the volume of the concrete block.
20cm

31. A container for oil is in the shape of a prism.
The width of the container is 9 centimetres.
The uniform cross section of the container consists of a rectangle and a
triangle with dimensions as shown.
9cm
28c
m
32-5 cm
Calculate the volume of the container, correct to the nearest
litre.

32. A flower planter is in the shape of a prism.
The cross-section is a trapezium with dimensions as shown.
3Ocm
32 cm
(n) Calculate the area of the cross-section of the
planter.
{b) The volume of the planter is 156 litres.
b8 cm
I centimetres
Calculate the length, I centimetres, of the planter.

33. Lemonade ie to be poured from a 2 litre bottle into glasses.
Each glass is in the shape of a cylinder of radiua 3 centimetres and height
g centimetres.
litres
How many full glaaees can be poured from the bottle i

34. A concrete ramp is tn be built.
The mmp is in the shape of a
cuboid and a triangular prism with dimensions as
shown.
0•5 m
2m
(o) Calculate the value of x.
(h) Calculate the volume of concrete required to build the ramp.

35. 5. A feeding trough, 4 metres long, is prism-
shaped.
The uniform cross-section is made up of a rectangle end semi-
circle ushown below.
0-25 m
Find the volume of the trough, correct to 2 significant figures.

36. (6) Another paperweight, in the shape of a
hemisphere, is filled with sand.
It contains the same volume of sand as the first paperweight.
Calculate the radius of the hemisphere.
[The volume of a hemisphere with radius r is given by
the formula,

37. a) A hlock of copper 18 ccntimetres long
is prism shaped as shown.
25
cm*
The arca of its cross section is 28 square
centimetres. Find the volume of the block.
{b) The block is melted down to make
a cylindrical cable of diameter 14 millimetres.
Calculate the length of the cable.
18
cm

38. 6. A io hold chocolates is in the
shape of part of a cone with dimensions as
show n below.
1 6 cm
)2 rm
Calculate the volurnc f›f the container.
Gix’C j'CUi T 'answer correct to one significant figure.

39. 3. A child's toy is in the shape of a
hemisphere with a cone on top,
as shown in the diagram.
The toy is 10 centimetres wide
and 16 centimetres high.
Calculate the volume of the toy.
Give your answer
correct to 2 significant figures.
10c
m
16
cm
5

40. b. A parden trough is in the shape of a prism.
25 cm
The height of the trough is 25 centimetres.
The cross-section of the trough consists of a rectangl e and two semi-circles
with rrieasurements as shown.
$30cm
(‹z) Find the volume of the garden trough in cubic centimetres.
Giv e rou r ins wcr correct to two st gn iticani figures.

41. t
0
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t h e crc›ss- sec t ici n cif c›ne cif che cvihes is sRc iw n in the clia rarri belc›w•.
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i
i
i
7
4 rr›m
th e i n n e r cliarrne te is 7A rriillirnecres.
th e c›vicer cliarne ter is B2 rriillirnecres.
t h . e c o d e is TOO mi ll irn et re s l o n g .

42. A cylindrical container has a volume of
3260 cubic centimetres.
The radius of the cross section is
6-4 centimewee.
Calculate the height of the cylinder.

43. (s) Cî/Cllâte the Y
0
l
X
I
l
e 0(tËe fllüg.
ìß nillilitrßî 0ÍC0((ëë êfë ğ0ßfëJ
Ífl.
CalculstetŁedeptłt0fth4¢0ffeeintŁecvp.
+-!0cm-
+

44. 7. A pharmaceutical company makes
vitamin pills in the shape of spheres of radius 0 5
centimetres.
(n) Calculate the volume of one pill.
Give your answer correct to two significant figures.
The company decides to change the shape of
each pill to a cylinder,
{b) The new pill has the same volume as the original and its diameter is
1 4 centimetres.
Calculate the height of the new' pill.

45. 5. A glass ornament in the shape of a cone is partly filled with coloured water.
30cm
The come is 24 ce n timetres h igh and has a base of diameter 3()
centimetres.
The water is 1 6 centimetres deep and measures 1(I centimetres across
the
top.
What is the volume of the water?
Give your answer correct to 2 significant figures.
24 cm