10. Find the volume of each of the following solids. (i)
2 3
m
2cm 5
3 4
m
2 9
mm
11. Mohammed needs to change the water in his goldfi sh tank. The dimensions of the tank are as follows: length = 0·8 m, width = 0·6 m and height = 0·5 m
He uses a cube-shaped bucket to fi ll the tank. The bucket has a side length of 0·2 m. (i)
If 1 m3 = 1 000 litres of water, how many
litres of water does (a) the goldfi sh tank hold? (b) the bucket hold?
(ii) Calculate how many times Mohammed must fi ll the bucket to completely fi ll his goldfi sh tank.
17.4 Volume of a cylinder
A roll of kitchen paper, a copper pipe, a tube of crisps, and a can of soup all have something in common: they are all cylinders.
A cylinder is a three-dimensional solid in geometry.
A cylinder is a curved shape, and has two ends in the shape of circles. These circles always have the same radius. A cylinder can be solid all the way through or hollow, like a pipe.
Some every day examples of cylinders include: Discuss and discover
When we analysed the volume of a rectangular solid, we discovered that the volume can be found by fi nding the area of its base and multiplying that by its height.
1. Use this method to fi nd the volume of the cylinder shown.
2. Can you now write down a formula for fi nding the volume of a cylinder of radius r and height h?
3. Explain why the volume formulae V = πr2 h and V = b × h give the same results. (b represents the area of the base.) radius = 7 cm
By the end of this section you should: ● understand how to calculate the volume of a cylinder ● be able to solve problems involving volume of cylinders