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. Since the base is a circle and the area of a circle is πr2 then the volume of the cylinder is πr2 × h.
Volume of cylinder = πr2h
Surface Area of cylinder = 2πr2 + 2πrhWorksheet - Calculate volume of cylinders
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) V = Area of base × height
Sometimes you may be required to calculate the volume of a hollow cylinder or tube or pipe.
Volume of hollow cylinder:
= πR2 h – πr2 h
= πh (R2– r2)
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.
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
How to find the volume of a cylinder in a prism?
A cylindrical can is packed securely in a box.
a) Find the radius and height of the can.
b) What is the volume of the empty space between the can and the box?
c) Find the ratio of the volume of the can to the volume of the box.
These videos show how to solve word problems about cylinders.Examples:
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