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Volume of a Cylinder

Volume of a Cylinder

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.

Volume of a cylinder

Example 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.

For a circle: Area `= pir^2`
Substitute `A` `= pi xx 2^2`
`= 4pi`

The cross-sectional area is `4pi`

For a cylinder: Volume = area xx length
Substitute V `= 4pi xx 42`
`= 527.79`

Answer: 527.8 cm3

Example 2

What is the diameter of a cylinder with a volume of 1000cm3 and a length of 100cm? Give the answer correct to 1 decimal place.

For a Cylinder Volume `= pir^2l`
Substitute `1000` `= pir^2 xx 100`
Divide both sides by 100 10 `= pir^2`
Divide both sides by `pi` 3.183 `= r^2`
Square root 1.784 `= r`

Answer: 1.8cm