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Volume of a Cylinder

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formula

  • Volume of a Cylinder = πr2h.

notes

Volume of a Cylinder:

The volume of a cylinder can be obtained as: base area × height

= area of circular base × height = πr2h

So, the Volume of a Cylinder = πr2h, where r is the base radius and h is the height of the cylinder.

Example

A rectangular paper of width 14 cm is rolled along its width and a cylinder of radius 20 cm is formed. Find the volume of the cylinder. (Take `22/7` for π)

A cylinder is formed by rolling a rectangle about its width. Hence the width
of the paper becomes height and the radius of the cylinder is 20 cm.
Height of the cylinder = h = 14 cm
Radius = r = 20 cm
Volume of the cylinder = V = πr2h
= `22/7` × 20 × 20 × 14
= 17600 cm3
Hence, the volume of the cylinder is 17600 cm3.

Example

A rectangular piece of paper 11 cm × 4 cm is folded without overlapping to make a cylinder of height 4 cm. Find the volume of the cylinder.
Length of the paper becomes the perimeter of the base of the cylinder and
width becomes height.
Let radius of the cylinder = r and height = h
Perimeter of the base of the cylinder = 2πr = 11
or `2 xx 22/7 xx r = 11`
Therefore,
r = `7/4` cm
Volume of the cylinder = V = πr2h
= `22/7 xx 7/4 xx 7/4 xx 4` cm3
= 38.5 cm3
Hence the volume of the cylinder is 38.5 cm3.
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