GRE PREP: Volume of sphere

# GRE PREP: Volume of sphere

426.1k points

How many times greater is the volume of a sphere with radius of 3 than the volume of a sphere with radius $\sqrt{3}$?

GRE PREP
LanceJ

426.1k points

The formula for the volume of a sphere is,

$V = \frac{4}{3}\pi r^3$

let,

$V_1$ = volume of the sphere with radius 3
$V_2$ = volume of the sphere with radius $\sqrt{3}$

then to get how many times greater $V_1$ is than $V_2$ we want to take,

$\frac{V_1}{V_2} = \frac{ \frac{4}{3}\pi (3)^3}{\frac{4}{3}\pi (\sqrt{3})^3}=\frac{3^3}{\sqrt{3}^3}=\frac{27}{\sqrt{27}}=\frac{27}{3\sqrt{3}}=\frac{9}{\sqrt{3}}=3\sqrt{3}$

The volume of the sphere with radius 3 is $3\sqrt{3}$ times bigger

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