Question

A cylinder and hemisphere have the same radius. Their combined height is 30 cm. If the cylinder and hemisphere have equal volumes, find the radius.

• A. 12 cm
• B. 15 cm
• C. 16 cm
• D. 18 cm

Answer 1

Answer:

D. 18 cm

Let the common radius be (r) cm.

The combined height is 30 cm.

So, if the cylinder's height is (h),

[
h+r=30
The volumes are equal.

For the cylinder:

$\pi r^2h$

For the hemisphere:

$\frac{2}{3}\pi r^3$

Equating the volumes:

$\pi r^2h=\frac{2}{3}\pi r^3$
$h=\frac{2r}{3}$

Substitute into (h+r=30):

$\frac{2r}{3}+r=30$

$\frac{5r}{3}=30$

$r=18\text{ cm}$