In KS3 Maths you'll spend a lot of time looking at shapes and their properties, 2-Dimensional shapes, polygons, have areas which can be worked out. But 3-Dimensional shapes, polyhedrons, have another property - their volume or capacity.

In a similar way to how 2-D shapes cover an area, 3-D shapes contain a volume. This is their capacity, or how much three-dimensional space the shape occupies or contains. The volume of a container is generally understood to be the capacity such as the amount of fluid that the container could hold. Think of a 2 litre bottle of water. It contains a volume or capacity of 2 litres or 2,000cm^{3}.

So, the volume of a 3-D shape is how much space it takes to fill it. Get your fill of volume and capacity with the following quiz. Take your time and be sure to consider your answers before choosing which ones are correct. Good luck!

1.

A cuboid has a volume of 72 cm^{3}. Its length is 6 cm and its width is 4 cm. What is the height of the cuboid?

3 cm

4 cm

6 cm

7 cm

72 cm = 6 cm x 4 cm x 3 cm (V = l x w x h)

2.

The volume of a cube is 125 cm^{3}. What is the length of each edge of the cube?

2.5 cm

5 cm

12.5 cm

25 cm

The cube root of 125 = 5 because 5 x 5 x 5 = 125

3.

An empty box can hold 100 smaller boxes each measuring 10 cm x 10 cm x 10 cm. How many litres of capacity does the empty box have?

10 litres

100 litres

500 litres

1,000 litres

1 litre = 1,000 cm^{3}. Each of the smaller boxes has a volume of 1 litre

4.

What is the volume of a cuboid with a length of 8 cm, a width of 4 cm and a height of 6 cm?

180 cm^{3}

18 cm^{3}

192 cm^{3}

219 cm^{3}

8 x 4 x 6 = 192

5.

Two cuboids have the same volume. The first measures 10 cm x 3 cm x 4 cm. The second measures 5 cm x 4 cm x what?

2 cm

4 cm

6 cm

8 cm

10 x 3 x 4 = 120 so 5 x 4 x ? = 120

5 x 4 = 20 so 20 x ? = 120

120 ÷ 20 = 6

5 x 4 = 20 so 20 x ? = 120

120 ÷ 20 = 6

6.

The volume of a cuboid is calculated using .......

length + width + height

length x width x height

length x width^{2}

length x width^{3}

V = l x w x h (V = lwh)

7.

The volume of a cylinder is calculated using .......

π r^{2} x length

π r^{3} x length

r^{2} x length

r^{3} x length

Work out the are of the circle on a cylinder using π r^{2} then times by the length of the cylinder

8.

A cuboid has a length of 10 cm, a width of 5 cm and a height of 15 cm. What is its volume?

250 cm^{3}

500 cm^{3}

750 cm^{3}

1,000 cm^{3}

1,000 cm = 10 cm x 5 cm x 15 cm (V = l x w x h)

9.

A tank has a length of 50 cm, a width of 60 cm and a height of 80 cm. How many litres of water can it hold?

120 litres

180 litres

240 litres

300 litres

50 cm x 60 cm x 80 cm = 240,000 cm^{3}. Then divide by 1,000 as 1 litre = 1,000 cm^{3}

10.

An oil drum (cylinder) measures 88 cm tall and has a diameter of 60 cm. Approximately how many litres can it hold?

49 litres

149 litres

199 litres

249 litres

60 cm diameter = 30 cm radius. 30^{2} = 900. 900 x 3.142 (π) = 2,827.8 Multiply this by 88 (height or length) = 248,846 cm^{3} or approximately 249 litres

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