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Volume of a Cone

Volume of a cone_1As we know, a cone is a pyramid with a circular base. The volume of a cone is calculated by multiplying the area of the circular base and its height and dividing by 3.

The formula for the volume of a cone calculation is –

V  =  1/3A h

= 1/3~*~pi r^2h    (pi r^2 is the area of the circular base)

 

Example 1 : Volume of the cone in the above figure

V  =  1/3A h

= 1/3~*~pi r^2h

=  1/3~*~pi 12^2~*~15

=  1/3~*~3.14~*~12~*~12~*~15

=  3.14 x 144 x 5

=  2260.8 cm3

 

Example 2 : What is the volume of the cone with base diameter 28 cm and height 25 cm.

V  =  1/3~*~ pi r^2~*~h

=  1/3 x 3.14 x 142 x 25    (r = 28/2 = 14 cm)

=  5128.7 cm3

 

When you are given the slant height of the cone (down the curved surface), use Pythagoras theorem to calculate the height of the cone before you calculate the volume.

Pythagoras theorem states that in any right-angled triangle, the square of the hypotenuse is equal to the sum of the squares on the other two sides.

Let’s look at this in the example below.

Example 3 : Calculate the volume of the cone shown in this diagram.

Volume of a cone_2First we need to find the height of the cone.

Height  =  sqrt{34^2~-~16^2}

=  sqrt{1156~-~256}

=  sqrt{900}

=  30 cm

Volume of a cone V  =  1/3~*~ pi r^2~*~h

=  1/3 x 3.14 x 16 x 16 x 30

=  8038.4 cm3