A cone is melted and recast into another cone with half the radius. Find the new height if the original height was 12 cm.
Show answer & explanation
Correct answer: A
Explanation
Given:
Original height (h₁) = 12 cm
New radius = half the original radius = r₁/2
By formula:
Volume of cone (V) = (1/3)πr₁²h
(1/3)πr₁²h₁ = (1/3)π(r₁/2)²h₂
r₁² × 12 = (r₁² / 4) × h₂
12 = h₂/4
h₂ = 48 cm