Two hemispheres of radii 6 cm and 8 cm are melted and recast into a single hemisphere. What is the approximate radius of the new hemisphere formed?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 9 cm.
Volume of a hemisphere = (2/3)πr3
Total volume = (2/3)π(63 + 83) = (2/3)π(216 + 512) = (2/3)π × 728
Let the radius of the new hemisphere = R cm
(2/3)πR3 = (2/3)π × 728
⇒ R3 = 728
⇒ R ≈ 9 cm