A sphere is melted and recast into 8 identical cones, each with radius 3 cm and height 4 cm. What was the radius of the original sphere?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 4.16 cm.
Volume of 1 cone = (1/3)πr2h = (1/3)π × 32 × 4 = 12π cm3
8 cones volume = 8 × 12π = 96π cm3
Volume of sphere = 96π cm3
Let the radius of the sphere = R cm
(4/3)πR3 = 96π
⇒ (4/3)R3 = 96
⇒ R3 = 96 × 3/4 = 72
⇒ R = ∛72 ≈ 4.16 cm