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Volumes of prisms and surface areas
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Volumes and surface area
BTEOTSSBAT solve problems involving volume and surface area
Key wordsvolumecross sectionprismcubecuboidcylinder
Volume is the amount of space a solid object takes up. The units are mm³, cm³, m³, km³ and so on
Convert m³ into cm³
Volume is the amount of space a solid object takes up. The units are mm³, cm³, m³, km³ and so on
Convert m³ into cm³
A box has a volume of 0.5 m³.It needs to fit into a bag of size 100 000 cm³. Will it fit?
Volume is the amount of space a solid object takes up. The units are mm³, cm³, m³, km³ and so on
Convert m³ into cm³
A box has a volume of 0.5 m³.It needs to fit into a bag of size 100 000 cm³. Will it fit?
0.5 m³ = 0.5 m x m x m
Volume is the amount of space a solid object takes up. The units are mm³, cm³, m³, km³ and so on
Convert m³ into cm³
A box has a volume of 0.5 m³.It needs to fit into a bag of size 100 000 cm³. Will it fit?
0.5 m³ = 0.5 m x m x m
x 100
Volume is the amount of space a solid object takes up. The units are mm³, cm³, m³, km³ and so on
Convert m³ into cm³
A box has a volume of 0.5 m³.It needs to fit into a bag of size 100 000 cm³. Will it fit?
0.5 m³ = 0.5 m x m x m
= 50 cm x m x m
x 100
Volume is the amount of space a solid object takes up. The units are mm³, cm³, m³, km³ and so on
Convert m³ into cm³
A box has a volume of 0.5 m³.It needs to fit into a bag of size 100 000 cm³. Will it fit?
0.5 m³ = 0.5 m x m x m
= 50 cm x m x m
x 100
x 100
Volume is the amount of space a solid object takes up. The units are mm³, cm³, m³, km³ and so on
Convert m³ into cm³
A box has a volume of 0.5 m³.It needs to fit into a bag of size 100 000 cm³. Will it fit?
0.5 m³ = 0.5 m x m x m
= 50 cm x m x m
x 100
x 100
= 5000 cm x cm x m
Volume is the amount of space a solid object takes up. The units are mm³, cm³, m³, km³ and so on
Convert m³ into cm³
A box has a volume of 0.5 m³.It needs to fit into a bag of size 100 000 cm³. Will it fit?
0.5 m³ = 0.5 m x m x m
= 50 cm x m x m
x 100
x 100
x 100
= 5000 cm x cm x m
Volume is the amount of space a solid object takes up. The units are mm³, cm³, m³, km³ and so on
Convert m³ into cm³
A box has a volume of 0.5 m³.It needs to fit into a bag of size 100 000 cm³. Will it fit?
0.5 m³ = 0.5 m x m x m
= 50 cm x m x m
x 100
x 100
x 100
= 5000 cm x cm x m
= 500 000 cm x cm x cm = cm³
Volume is the amount of space a solid object takes up. The units are mm³, cm³, m³, km³ and so on
Convert m³ into cm³
A box has a volume of 0.5 m³.It needs to fit into a bag of size 100 000 cm³. Will it fit?
0.5 m³ = 0.5 m x m x m
= 50 cm x m x m
x 100
x 100
x 100 So, no it won’t fit! = 5000 cm x cm x m
= 500 000 cm x cm x cm = cm³
PrismsShapes that have a uniform cross section (ie all the same all the way through) are called prisms.
The volume of a prism is the cross-sectional area length.
A square prism is called a cube
A square prism is called a cube
A rectangular prism is called a cuboid
A square prism is called a cube
A rectangular prism is called a cuboid
A circular prism is called a cylinder
Now try these
1. Find the volume of the following cuboids 4 cm2 cm high 3 cm wide 2 cm
5 cm 3 cm
2. Computer disks are 9 cm by 0.3 cm by 9.3 cm. Calculate the volume of the disk.
3. A tin of beans has a diameter of 7 cm and is 4.5 cm high. Work out the volume of the tin.
Surface area
All 3D shapes have a surface area.
The surface area is the sum of the area of all the sides of a shape.
The surface area of a cuboid is the sum of all the 6 rectangular faces.
The rectangular faces can be grouped in pairs.
ExampleFind the surface area of the cuboid which is 4 cm 5 cm 10 cm
Side number Area
1 and 2
3 and 4
5 and 6
ExampleFind the surface area of the cuboid which is 4 cm 5 cm 10 cm
Side number Area
1 and 2
3 and 4
5 and 6
ExampleFind the surface area of the cuboid which is 4 cm 5 cm 10 cm
Side number Area
1 and 2 4 5 = 20
3 and 4
5 and 6
ExampleFind the surface area of the cuboid which is 4 cm 5 cm 10 cm
Side number Area
1 and 2 4 5 = 20
3 and 4
5 and 6
ExampleFind the surface area of the cuboid which is 4 cm 5 cm 10 cm
Side number Area
1 and 2 4 5 = 20
3 and 4 4 10 = 40
5 and 6
ExampleFind the surface area of the cuboid which is 4 cm 5 cm 10 cm
Side number Area
1 and 2 4 5 = 20
3 and 4 4 10 = 40
5 and 6 (round the back)
ExampleFind the surface area of the cuboid which is 4 cm 5 cm 10 cm
Side number Area
1 and 2 4 5 = 20
3 and 4 4 10 = 40
5 and 6 5 10 = 50
ExampleFind the surface area of the cuboid which is 4 cm 5 cm 10 cm
Side number Area
1 and 2 4 5 = 20
3 and 4 4 10 = 40
5 and 6 5 10 = 50
Total of the 3 pairs of sides
ExampleFind the surface area of the cuboid which is 4 cm 5 cm 10 cm
Side number Area
1 and 2 4 5 = 20
3 and 4 4 10 = 40
5 and 6 5 10 = 50
Total of the 3 pairs of sides 110
ExampleFind the surface area of the cuboid which is 4 cm 5 cm 10 cm
Side number Area
1 and 2 4 5 = 20
3 and 4 4 10 = 40
5 and 6 5 10 = 50
Total of the 3 pairs of sides 110
2 (for all sides) 220 cm²
ExampleFind the surface area of the cuboid which is 4 cm 5 cm 10 cm
Now try these
1. Find the surface area of the following cuboids 4 cm2 cm high 3 cm wide 2 cm
5 cm 3 cm
2. Computer disks are 9 cm by 0.3 cm by 9.3 cm. Calculate the surface area of the disk.
3. A tin of beans has a diameter of 7 cm and is 4.5 cm high. Work out the surface of the tin.
