Asked by LanceJ 2 years ago

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

Answered by LanceJ 2 years ago

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**

Surround your text in `*italics*`

or `**bold**`

, to write a math equation use, for example, `$x^2+2x+1=0$`

or `$$\beta^2-1=0$$`

Stats

Views: 32

Asked: 2 years ago