Volume of a Sphere

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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

Next: Volume of a Cone