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.

Correct option is D

​Given :

Cylinder and hemisphere have the same radius = r

Total height = 30 cm

Height of hemisphere = r

Therefore, height of cylinder = 30 – r

Volumes are equal.

Formula Used :

Volume of cylinder:
​$$V_c = \pi r^2 h$$​​

Volume of hemisphere:
​$$V_h = \frac{2}{3}\pi r^3$$

Solution:

Given:
​$$\pi r^2(30 - r) = \frac{2}{3}\pi r^3$$​​

3$$0 - r = \frac{2}{3} r$$​​

30 = r $$+ \frac{2}{3}r = \frac{5}{3}r$$​​

r = 30$$\times \frac{3}{5}$$​​

r = 18 cm