Question

If the surface area of a sphere is $36\pi {cm}^2$, then the volume of the sphere is equal to

• A. $12\pi {cm}^3$
• B. $36\pi {cm}^3$
• C. $72\pi {cm}^3$
• D. $108\pi {cm}^3$

Answer 1

Answer: (B)

$36\pi {cm}^3$

We have,

$surfacearea=36\pi c{m}^2$

We know that the surface area of the sphere

$=4\pi r^2$

So,

$4\pi r^2=36\pi$

$r^2=9$

$r=3cm$

We know that the volume of the sphere

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

Therefore,

$=\frac{4}{3}\pi \times 3^3$

$=4\times \pi \times 9$

$=36\pi c{m}^3$

Hence, this is the answer.