Question

A section of guttering can hold up to 20 litres of rainwater. The diameter is 11cm. Work out the length in metres.

Answer 1

2.1 m

Explanation:

The gutter is in the shape of a cylinder.

Its volume is 20 liters and its diameter is 11 cm (0.11 m).

Its radius is half of its diameter => r = 0.055 m.

The volume in cubic metres:

1 litre = 0.001 cubic metres

20 litres = 20 * 0.001 = 0.02 cubic metres

The volume of a section of guttering is given as:

`V = \pi r^2h`

where h = length of the guttering

Therefore:

`0.02 = \pi * 0.055^2 * h\\\\0.02 = 0.009503h\\\\h = 0.02 / 0.009503\\\\h = 2.10 m`

The length of the section of guttering is 2.1 m long.