A hemisphere of radius 30 cm is molded to form a cylinder of height 180 cm. The diameter of the cylinder is:

A hemisphere of radius 30 cm is molded to form a cylinder of height 180 cm.

Let's assume the radius of hemisphere and cylinder are $$r_h$$ and $$r_c$$ respectively.

$$r_h = 30$$ cm

height of cylinder = h = 180 cm

Volume of hemisphere =  Volume of cylinder

$$\frac{2}{3}\times\ \pi\ \times\ \left(r_h\right)^3=\pi\ \times\ \left(r_c\right)^2\times\ h$$

$$\frac{2}{3}\times\ \left(30\right)^3=\left(r_c\right)^2\times\ 180$$

$$\frac{2}{3}\times27000=\left(r_c\right)^2\times\ 180$$

$$2\times9000=\left(r_c\right)^2\times\ 180$$

$$18000=\left(r_c\right)^2\times\ 180$$

$$100=\left(r_c\right)^2$$

$$10^2=\left(r_c\right)^2$$

$$r_c = 10$$ cm

The diameter of the cylinder = $$2\times\ r_c$$

= $$2\times10$$

= 20 cm