Question

This cylinder is 6 inches tall & has a volume of 60πin^3. Find the area of the cross section

Answer 1

Given:

Height of cylinder = 6 inches

Volume of cylinder = 60π in³

To find:

The area of the cross section.

Solution:

Volume of cylinder:

$V=\pi r^2h$

$\pi r^2h=60\pi$

Cancel the common factor π on both sides.

$r^2h=60$

Substitute h = 6.

$r^2\times 6=60$

Divide by 6 on both sides, we get

$r^2=10$

Taking square root on both sides.

$r=\sqrt{10}$ inch

Area of cross section = $\pi r^2$

                                   $=\pi (\sqrt{10} )^2$    

                                   $=10 \pi$ in²

The area of the cross section is 10π in².