3. The volume of a solid is the amount of space occupied by the solid.
The greater the volume of a solid the more space it takes up.
The volume of a solid is the number of unit cubes that the solid can be
divided into.
1 unit
1 unit
1 unit
2 units
3 units
4 units
24 unit cubes
altogether
4. This cuboid is made up of centimetre cubes
(cm³). What is its volume?
12 cm³
5. 5 cm
10 cm
2 cm
What is the volume of this cuboid?
100 cm³
6. 6 m
3 m
2 m
What is the volume of this cuboid?
36 m³
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8. Answers
1)5 x 2 x 7 = 70 cm3
2)3 x 2 x 8 = 48 cm3
3)5 x 6 x 2 = 60 cm3
4)2 x 2 x 6 = 24 cm3
5)5 x 2 x 3 = 30 cm3
6)2 x 7 x 4 = 56 cm3
7)7 x 7 x 2 = 98 cm3
8)2 x 4 x 5 = 40 cm3
9)2 x 9 x 2 = 36 cm3
Extension question:
54 ÷ (9 x 2)
= 54 ÷ 18
= 3cm
9. Josh is having a birthday party! He wants to make boxes of
sweets to give to his guests.
He starts with a square piece of paper that measures 20cm
x 20cm. How big should the squares be that he cuts out of
the corners to maximise the volume of the box?
11. Extension questions
1. What if the square you cut out doesn’t
have to use whole number measurements
(e.g. 2.4cm)? Would this change your
answer?
2. What if you started from a 10cm x 20cm
rectangle instead? What would the
biggest volume be?
12. Surface areas of cubes and cuboids
What is surface area?
Think about finding the
area of a square or
rectangle…
width
height
Area = height x width
What about if we phrase surface area differently…
The area of the surface
13. The area of the surface
How could we find the
surface area of a cuboid
using the height, width
and length?
H
L
W
How many faces does a
cuboid have? 6
So we could add together the areas of all 6 faces!
Surface areas of cubes and cuboids
14. H
L
W
Surface area =
(Length x Height) +
(Length x Height) +
(Height x Width) +
(Height x Width) +
(Length x Width) +
(Length x Width)
Front
Back
Left
Right
Top
Bottom
Top
Right
Front
Left
Bottom
Back
By adding the area of all of the faces, we can find the
surface area of the whole cuboid.
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17. A cube is cut out
of a larger cube
and stuck into
the corner, as
shown. What is
the surface area
of the resulting
shape?
All lengths are in
centimetres
26. Volume of a prism
= area of cross-section x vertical height
Cross-section
Vertical height
27. Example: Find the volume of this prism
25 cm2
7 cm
Volume of a prism
= area of cross-section x vertical height
25 x 7 = 175 cm³
28. Example: Find the volume of this prism
3 cm
6 cm
10 cm
Volume of a prism
= area of cross-section x vertical height
Area of cross-section = ½ x 6 x 3
Volume = 9 x 10
cm²
= 9
= 90 cm³
30. Thoughts and crosses
Calculate the volumes of 4 of the
prisms, either vertically, horizontally or
diagonally
Volume of Prisms
31. The area of the surface
How could we find the
surface area of a
triangular prism using the
height, width, depth and
slant height?
How many faces does a
triangular prism have? 5
So we could add together the areas of all 5 faces!
H
D
W
S
32. Surface area =
(Width x Height ÷ 2) +
(Width x Height ÷ 2) +
(Height x Depth) +
(Slant x Depth) +
(Width x Depth)
Front
Back
Left
Right
Bottom
By adding the area of all of the faces, we can find the
surface area of the whole triangular prism.
H
D
W
S
Right
Front
Left
Bottom
Back
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35. How confident do you feel with this topic?
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36. Starter
Calculate the areas and circumferences of these circles to 1 d.p.
Q1 Q2 Q3
Q6
Q4 Q5
7 cm
4.5
cm
8 cm
3 cm
2.5 cm
2 cm
37. Answers
Q1 A = 38.5 cm², C = 22.0 cm
Q2 A = 19.6 cm², C = 15.7 cm
Q3 A = 50.3 cm², C = 25.1 cm
Q4 A = 12.6 cm², C = 12.6 cm
Q5 A = 28.3 cm², C = 18.8 cm
Q6 A = 15.9 cm², C = 14.1 cm
38. Calculate the volume of this cylinder. Give your answer to 3 s.f.
Volume of a prism = area of cross section x length
Area of cross-section = π x 12²
= 452.389… cm²
Volume = 452.389… x 20
= 9047.8 cm³
Area of cross-section = π x 5²
= 78.539… cm²
Volume = 78.539… x 12
= 943 cm³
Calculate the volume of this cylinder. Give your answer to 1 d.p.
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42. Surface area of curved part of cylinder = πdh
Area of top circle = πr²
Area of bottom circle = πr²
Surface area of cylinder = 2πr² + πdh
43. 4cm
6cm
Calculate the total surface
area of the cylinder, giving
your answer to 1 d.p.:
Top = π x 2² = 12.566… cm²
Curved = π x 4 x 6 = 75.398… cm²
Bottom = π x 2² = 12.566… cm²
Total = 12.566… + 75.398… + 12.566…
= 100.5 cm²
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