Two identical solid hemispheres, each with a radius of 21 cm, are melted and recast into a single sphere. What is the radius of the new sphere formed?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is Option 2 i.e. 21 cm.
Volume of one hemisphere = (2/3)πr3 = (2/3)π × 213 = (2/3)π × 9261 = 6174π cm3
Two hemispheres volume = 2 × 6174π = 12348π cm3
Volume of new sphere = (4/3)πR3 = 12348π
⇒ R3 = 12348 × 3/4 = 9261
⇒ R = ∛9261 = 21 cm