A solid metallic sphere of radius 4.2 cm is melted and…

A solid metallic sphere of radius 4.2 cm is melted and recast into a right circular cylinder of radius 6 cm. What is the height (in cm) of the cylinder (correct to one decimal place)?

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 2.7.

Volume of sphere = ${4\over3}\pi r^3$

⇒ ${4\over3}\pi (4.2)^3$

Volume of cylinder = πr²h

⇒ π(6)²h

Volume of sphere = Volume of cylinder

⇒ ${4\over3}\pi (4.2)^3$ = π(6)²h

⇒ ${4\over3}(4.2)^3$ = (6)²h

⇒ h = 2.7 cm

SSC Selection Post 2020 PYQ — Question 54