Single correct option
A solid metal sphere of radius 6 cm is melted and recast into a right circular cone with base radius 6 cm. What is the height of the cone?
- A. 18 cm
- B. 24 cm
- C. 27 cm
- D. 36 cm
Show answer and solution
Answer: (B) 24 cm
Volume is conserved when a solid is recast.
(4/3)π(6)³ = (1/3)π(6)²h.
Cancel π/3 and 36 from both sides: 4 × 6 = h, so h = 24 cm.
Tip: when the sphere and cone have the same radius r, h = 4r.
(4/3)π(6)³ = (1/3)π(6)²h.
Cancel π/3 and 36 from both sides: 4 × 6 = h, so h = 24 cm.
Tip: when the sphere and cone have the same radius r, h = 4r.
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