Volume of a cylinder


In this lesson, you'll learn how to calculate the volume of a cylinder.


What is a cylinder?

It's a three dimensional shape comprising two equal circular ends and a curved surface.



And the volume of a cylinder?

This is the amount of three dimensional space occupied by the cylinder.


Volume of cylinder formula

Cylinder volume  =  area of one of circular ends  x  height



The area of each cylinder end is πr² (where π = pi and r = radius of circle) - see also area of a circle.


So if h = cylinder height, the formula becomes



where Vcylinder = volume of cylinder.


Have you noticed the volume of a cone (πr²h) is three times the volume of a cylinder (1/3 x πr²h)? Given the same radius and height, you can fit three cones into one cylinder! 


Worked example

What's the volume of a cylinder with radius (r) 3cm and height (h) 4cm (where cm = centimeters)?


Vcylinder

=   πr²h

=   π  x  3²  x  4

=  113.1cm³ (cubic centimeters) to 1 d.p. (one decimal place)


Square the radius r on your calculator using x². In order, enter pi sign (π), multiply sign (x), 3, x², multiply sign (x), 4, equals sign (=). The display should show 113.0973355 which is 113.1 to 1 d.p. You may need to use a shift or 2nd function button on your calculator to access x² and π.


Now consider a cylinder with radius (r) 6m and height (h) 8m (where m = meters)


Vcylinder

=   πr²h

=   π  x  6²  x  8

=   904.78m³ (cubic meters) to 2 d.p. (two decimal places)


Grab your calculator again - press pi sign (π), 6, x², multiply sign (x), 8, equals sign (=).


Over to you!


Use different values for radius (r) and height (h) to calculate the volumes of cylinders of varying size.


Your answers should include appropriate units (for example, cubic centimeters cm³, cubic meters m³), together with the number of decimal places (d.p.) to which you are rounding.


Once you feel confident, move on to the next lesson - how to work out the surface area of a cylinder.


For further related lessons click:

Volume of a cone

Surface area of a cone


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