Question

The volume V of a sphere is given by V(r)=43r3 where r is the length of the radius. Write a function that gives the radius in terms of the volume.

Answer 1

Answer: $r=\sqrt[3]{\dfrac{3V}{4\pi}}$

Step-by-step explanation:

Given

The volume of a sphere is given by

$V(r)=\dfrac{4}{3}\pi r^3$

Now isolating $r^3$

Divide both sides by $\dfrac{4}{3}\pi$

$\Rightarrow \dfrac{V(r)}{\frac{4}{3}\pi }=r^3\\\\\Rightarrow r^3=\dfrac{3V}{4\pi}\\\\\Rightarrow r=\sqrt[3]{\dfrac{3V}{4\pi}}$