Volume of Cylinders

Solid geometry is concerned with three-dimensional shapes. In this lesson, we will look at how to find the volume of cylinders and hollow cylinders.

Volume of Solid Cylinders

A cylinder is a solid with two congruent circles joined by a curved surface.

In the above figure, the radius of the circular base is r and the height is h. The volume of the cylinder is the area of the base × height.

Example:

Calculate the volume of a cylinder where:

a) the area of the base is 30 cm 2 and the height is 6 cm.

b) the radius of the base is 14 cm and the height is 10 cm.

Solution:

a)

b)

Volume of Hollow Cylinders

Sometimes you may be required to calculate the volume of a hollow cylinder or tube.

Volume of hollow cylinder:
= π R² h – π r² h
= π h (R²– r²)

Example:

The figure shows a section of a metal pipe. Given the internal radius of the pipe is 2 cm, the external radius is 2.4 cm and the length of the pipe is 10 cm. Find the volume of the metal used.

Solution:

The cross section of the pipe is a ring:
Area of ring = [ π (2.4)²– π (2)²]= 1.76 π cm²

Volume of pipe = 1.76 π × 10 = 55.3 cm³
Volume of metal used = 55.3 cm³

The following video shows how to find the volume of a cylinder.

The following video shows how to find the volume of a cylinder.

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