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How do I calculate the volume of a cone?

By Kris Boulton on the 11th of June, 2012

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    Volume of a cone


    Given the radius and h, the volume of a cone can be found by using the formula:

     

    Formula: Vcone = 1/3 × b × h

    cone-image



    b is the area of the base of the cone. Since the base is a circle, area of the base = pi × r2

    Thus, the formula is Vcone = 1/3 × pi × r2 × h

    Use pi = 3.14


    Example #1:

    Calculate the volume if r = 2 cm and h = 3 cm

    Vcone = 1/3 × 3.14 × 22 × 3

    Vcone = 1/3 × 3.14 × 4 × 3

    Vcone = 1/3 × 3.14 × 12

    Vcone = 1/3 × 37.68 

    Vcone = 1/3 × 37.68/1

    Vcone = (1 × 37.68)/(3 × 1)

    Vcone = 37.68/3 

    Vcone = 12.56 cm3 


    Example #2:

    Calculate the volume if r = 4 cm and h = 2 cm

    Vcone = 1/3 × 3.14 × 42 × 2

    Vcone = 1/3 × 3.14 × 16 × 2

    Vcone = 1/3 × 3.14 × 32

    Vcone = 1/3 × 100.48 

    Vcone = 1/3 × 100.48/1

    Vcone = (1 × 100.48)/(3 × 1)

    Vcone = 100.48/3 

    Vcone = 33.49 cm3 

    Refine By Pinaki Panda on the 16th of January, 2013

Suggested reading…

Calculate the volumes of cylinders, cones and spheres

How do I find the volumes of spheres, cones and cylinders?

The volume of an object is the amount of space it takes up. Here are the equations to find the volumes for each of these slightly trickier shapes.

Volume of a Cylinder V = πr2h

Volume of a Cone: V = 1/3 x r2h  (h is the perpendicular height)

Volume of a Sphere: V = 4/3 x r3

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