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Volume of a Sphere

Volume of a sphere_1As we are aware, a sphere is a three-dimensional shape with one curved surface. All points on the surface of a sphere are the same distance from its centre. This distance is the radius of the sphere.

 

The volume of a sphere with radius r units is calculated by multiplying pi with cube of the radius and 4, then dividing by 3.

V  =  4/3~*~pir3

V  =  4/3~*~pi~* (radius)3

 

Example 1 : What is the volume of a sphere with radius 8 cm?

Volume of a sphere  =  4/3~*~pir3

=  4/3x 3.14 x 83

=  2143.6 cm3 (correct to 1 decimal place).

 

Example 2 : What is the volume of a sphere with diameter 60 mm?

Volume of a sphere  =  4/3~*~pir3

=  4/3x 3.14 x 303 (since r = 30 mm)

=  113,040 mm3

 

Volume of a Hemisphere

Volume of a sphere_2As the name suggests, a hemisphere is half of a sphere; and the volume of a hemisphere is half the volume of a sphere.

So the formula for volume of a hemisphere

V  =  2/3~*~pir3

V  =  2/3~*~pi~* (radius)3

 

Example 3 : What is the volume of a hemisphere with radius 6 cm?

V  =  2/3~*~pir3

=  2/3x 3.14 x 63

=  452.2 cm3 (correct to 1 decimal place)

 

Example 4 : What is the volume of a hemisphere with diameter 20 m?

V  =  2/3~*~pir3

=  2/3x 3.14 x 103   (since r = 10 m)

=  2093.3 cm3 (to 1 decimal place)