A metal sphere of radius 18 cm is melted and recast into n identical solid hemispheres, each of radius 6 cm. Then, find the total curved surface area of all hemispheres combined.
Show answer & explanation
Correct answer: A
Explanation
Given:
Sphere's radius = 18 cm
Hemisphere's radius = 6 cm
Formula:
Volume of sphere = (4/3)πR³
Volume of hemisphere = (2/3)πr³
Curved surface area of hemisphere = 2πr²
(4/3)π(18)³ = n × (2/3)π(6)³
(4/3)π × 5832 = n × (2/3)π × 216
7776π = 144πn
n = 54
Combined curved surface area = n × 2πr²
= 54 × 2π × (6)² = 3888π cm²