Volume of a cone


Welcome to cone geometry!


Let's kick off with how to work out the volume of a cone.


Definition of a cone

A three dimensional shape made up of a flat circular base and a curved surface which tapers to a point called the apex.



For simplicity, we'll consider a right circular cone - one which has its apex directly above the center of its circular base.


Definition of volume of a cone

The amount of three dimensional space the cone occupies.


Volume of cone formula

Cone volume  =  1/3  x  circular base area  x  perpendicular height



If h = perpendicular height and given a cone's base is circular and the area of a circle is πr² (where π= pi and r = radius of circle), the formula becomes



where Vcone = volume of cone.


Example calculation

Use the above formula to calculate volume of cone with base radius (r) 3cm and perpendicular height (h) 4cm (where cm = centimeters).


Vcone

=   1/3  x  πr²h

=   1/3  x  π  x  3²  x  4

=   37.7cm³ (cubic centimeters) to 1 d.p. (one decimal place)


To square the radius r on your calculator use x². The key stroke sequence for the above example is 1, divide sign (÷), 3, multiply sign (x), pi sign (π), multiply sign (x), 3, x², multiply sign (x), 4, equals sign (=). 37.69911184 should be displayed which is 37.7 to 1 d.p. You may need to access x² and π via a shift or 2nd function button.


How about a cone with base radius (r) 6m and perpendicular height (h) 8m (where m = meters)?


Vcone

=   1/3  x  πr²h

=   1/3  x  π 6²  x  8

=   301.59m³ (cubic meters) to 2 d.p. (two decimal places)


Enter on your calculator 1, divide sign (÷), 3, multiply sign (x), pi sign (π), 6, x², multiply sign (x), 8, equals sign (=).


Have a go!


Work out the volumes for different size cones by varying the base radius (r) and perpendicular height (h) values.


Learn more here:

Surface area of a cone

Volume of a cylinder

Surface area of a cylinder


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