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.
Surface Area of cylinder = 2πr2 + 2πrh
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.
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 calculate the volume of the shaded area of a cylinder? The shape forms a tube or pipe.
These videos show how to solve word problems about cylinders.Examples:
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
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