Question

The volume of a sphere varies directly as the cube of its radius and its volume is 36 $\pi$ cm${}^3$. Find the volume of the sphere, when the diameter is doubled.

Answer 1

Let the radius be $r$ then

The volume of the given sphere is $36\pi c{m}^3$

The volume of every sphere is,

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

So we can equate the two volumes:

$\mathrm{\$36\backslash pi\; =4\backslash pi\; \backslash dfrac\{r^3\}\{3\}\$}$

Multiply both sides by $3$

$r^3=27$

$r=3cm$

Hence, this is the answer.