A spherical ball of radius 24 cm is melted and recast into identical hemispheres, each having a radius of 8 cm. Determine the combined curved surface area of all hemispheres.
Show answer & explanation
Correct answer: A
Explanation
Given:
Radius of the sphere = 24 cm
Radius of the hemisphere = 8 cm
According to the formulas:
Volume of the sphere = (4/3)πR³
Volume of the hemisphere = (2/3)πr³
Curved surface area of the hemisphere = 2πr²
Volume of the sphere = (4/3)π(24)³
= (4/3)π × 13824
= 18432π
Volume of one hemisphere = (2/3)π(8)³
= (2/3)π × 512
= (1024/3)π
Number of hemispheres = 18432π / ((1024/3)π)
= 18432 × 3 / 1024
= 54
Curved surface area of one hemisphere = 2π(8)² = 2π × 64 = 128π
Total curved surface area of all hemispheres = 54 × 128π = 6912π cm²