Question

The formula for the volume of a sphere is $V=\frac{4}{3}\pi r^3$, and the formula for the surface area of a sphere is $A=4\pi r^2$. If a sphere has a surface area of $36\pi$, what is its volume?

• A. $27\pi$
• B. $36\pi$
• C. $54\pi$
• D. $72\pi$

Answer 1

The correct option is B $36\pi$

Given formula for volume of a sphere is
$V=\frac{4}{3}\pi r^3$
Formula for surface area of sphere is
$A=4\pi r^2$
Given is the surface area of a sphere $=$ $36\pi$
$\therefore 36\pi =4\pi r^2$
$\therefore r^2=9$
$\therefore r=3$
Putting $r=3$ in the formula of volume to find volume:
$V=\frac{4}{3}\pi r^3$
$\therefore V=\frac{4}{3}\pi \left(3^3\right)$
$\therefore V=\frac{4}{3}\pi \left(27\right)$
$\therefore V=4\pi \left(9\right)$
$\therefore V=36\pi$