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# Volume of Sphere Formula

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Volume of a Sphere is a measurement of the occupied units of a Sphere. The volume of a Sphere is represented by cubic units like cubic centimeter, cubic millimeter and so on. Volume of a Sphere is the number of units used to fill a Sphere. Generally the volume of a solid is calculated as the area of the base times its height as long the area is constant throughout the height of the solid. But this concept can not be directly applied to find the volume of a sphere because the area changes with every cross section of the sphere. In the above diagram, let r be the radius of the sphere. Since the over all dimensions of both the sphere and the cylinder are the same, the height of the cylinder is 2r. Under this condition, Volume of a cylinder = Area of the base x Height of the cylinder. = πr2 x 2r = 2πr3
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Volume of Sphere Formula
Volume of Sphere Formula
Volume of a Sphere is a measurement of the occupied units of a Sphere. The volume of a
Sphere is represented by cubic units like cubic centimeter, cubic millimeter and so on. Volume
of a Sphere is the number of units used to fill a Sphere.
Generally the volume of a solid is calculated as the area of the base times its height as long
the area is constant throughout the height of the solid. But this concept can not be directly
applied to find the volume of a sphere because the area changes with every cross section of
the sphere.
In the above diagram, let r be the radius of the sphere. Since the over all dimensions of both
the sphere and the cylinder are the same, the height of the cylinder is 2r.
Under this condition,
Volume of a cylinder = Area of the base x Height of the cylinder.
= r2 x 2r
= 2r3

Math.Tutorvista.com
Page No. :- 1/4

Therefore, as per Archimedes formula the volume of the sphere is,
( )( 2r3) = ( )r3
placed on his tomb! (This wish was fulfil ed)
Given below are some examples to find the volume of a sphere
Example 1:
The sphere has a radius of 8.2 cm. Solve for volume of sphere.
Solution:
Given:
Formula:
Volume of the sphere (v) = 43 r3 cubic unit
= 43 x x (8.2)3
=43 x 3.14 x 551.368
Volume of the sphere (v) = 2308.39 cm3
Example 2: The sphere has radius of 8.3 m. Solve for volume of sphere.
Solution:

Math.Tutorvista.com
Page No. :- 2/4

Given:
Formula:
Volume of the sphere (v) = 43 r3 cubic unit
= 43 x x (8.3)3
=43 x 3.14 x 571.78
Volume of the sphere (v) = 2393.88 m3
1. The sphere has radius of 5.8m. Find the volume of sphere.
Volume (V) = 817.28 m3
2. The sphere has radius of 6.9 cm. Find the surface area and volume of sphere.
Volume (V) = 1376.05 cm3

Math.Tutorvista.com
Page No. :- 4/4

ThankYou
Math.TutorVista.com

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