GCSE(F), GCSE(H),

A **cylinder** is a circular prism. As with other prisms, the volume of a cylinder can be calculated using the cross-sectional area x length.

Th cross-section of a cylinder is a circle. As the area of a circle =`πr^2`, the volume of a cylinder is `πr^2l`, where `r` is the radius of the circular end, and `l` is the length of the cylinder.

1. What is the volume of a cylinder with a diameter of 4cm and a length of 42cm? Give your answer correct to 1 decimal place.

Answer: 527.8 cm^{3}

The radius of a circle is `frac(1)(2)` the diameter = `frac(1)(2) xx 4 = 2`cm

The cross-sectional area is `pir^2 = pi xx 2^2 = 4pi`

The volume of the cylinder = cross-sectional area x volume

`= 4pi xx 42`

= 527.79 cm^{3}

2. What is the diameter of a cylinder with a volume of 1000cm^{3} and a length of 100cm? Give the answer correct to 1 decimal place.

Answer: 1.8cm

Volume of a cylinder = `pir^2l`

`1000 = pir^2 xx 100`

`10 = pir^2`

`r^2 = 3.183`

r = 1.784

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