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Volume of a Sphere

Volume of a Sphere

The volume of a sphere is given by:

`V = frac(4)(3)pir^3`

Volume of a sphere

Example 1

What is the volume of a sphere of diameter 6 cm? Give your answer to 3 significant figures.

For a sphere: Volume `= frac(4)(3)pir^3`
Substitute `=frac(4)(3)pi(6)^3`
`= 904.778`

Answer: 905 cm3

Example 2

A sphere and a cylinder have the same volume. If the radius of the sphere is 9cm, what is the height of the cylinder?

Cylinder: Volume `= pir^2l`
Sphere: Volume `= frac(4)(3)pir^3`
Both equal `pir^2l` `= frac(4)(3)pir^3`
Divide both sides by `pi` `r^2l` `= frac(4)(3)r^3`
Divide both sides by `r^2` `l` `= frac(4)(3)r`
Substitute `l` `= frac(4)(3)(9)`
`= 12`

Answer: 12 cm