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?

Given:

A solid metallic hemisphere of radius 5.4 cm is melted and recast into a right circular cylinder of radius 12 cm.

Formula used:

Volume of hemisphere = \(\dfrac{2}{3}\pi r^3\)

Volume of cylinder = \(\pi r^2 h\)

Calculation:

Volume of hemisphere = Volume of cylinder

\(\dfrac{2}{3}\pi (5.4)^3\) = \(\pi (12)^2 h\)

⇒ \(\dfrac{2}{3} \times (5.4)^3 = (12)^2 h\)

⇒ \(\dfrac{2 \times 157.464}{3} = 144h\)

⇒ \(\dfrac{314.928}{3} = 144h\)

⇒ 104.976 = 144h

⇒ h = \(\dfrac{104.976}{144}\)

⇒ h = 0.729

∴ The correct answer is option (2).