A solid metallic hemisphere of radius 5.4 cm is melted and recast into a right circular cylinder of radius 12 cm. What is the height (in cm) of the cylinder?

Correct option is B

Given:

Radius of hemisphere: r = 5.4 cm

Radius of cylinder: R = 12 cm

Volume of hemisphere is converted into volume of cylinder.

Formula Used:

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

Volume of cylinder = $$\pi R^2 h$$​​

Solution:

Equating volumes,

​$$\frac{2}{3} \pi (5.4)^3 = \pi (12)^2 h \\ \ \\\frac{2}{3} \times (5.4)^3 = 144h\\ \ \\ \implies h = \frac{2\times (5.4)^3}{3\times 144}$$​​

h = 0.729 cm