Volume of a Sphere

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.

Formula for Volume of a Sphere was found by Archimedes. Archimedes found after several experiments that the volume of a sphere and also its surface area is exactly `(2)/(3)` ^rd of the volume and the surface area of a cylinder with the same outer dimensions.

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

Therefore, as per Archimedes formula the volume of the sphere is,

(`(2)/(3)` )( 2πr³) = (`(4)/(3)` )πr³

So much happy about this result by himself, Archimedes wished a cylinder and globe be placed on his tomb! (This wish was fulfilled)

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:

Radius (r) = 8.2 cm

Formula:

Volume of the sphere (v) = 43 π r³ cubic unit

= 43 x π 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:

Given:

Radius (r) = 8.3 m

Formula:

Volume of the sphere (v) = 43 π r³ cubic unit

= 43 x π 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.

Answer:

Volume (V) = 817.28 m³

2. The sphere has radius of 6.9 cm. Find the surface area and volume of sphere.

Answer:

Volume (V) = 1376.05 cm³