When the radius of a sphere is increased by 7 cm, its surface area increases by 4312 cm². What is the volume (in cm³) of the original sphere? (Take π = 22/7)
Show answer & explanation
Correct answer: C
Explanation
Given:
Increase in radius = 7 cm
Increase in surface area = 4312 cm²
Surface area of the sphere = 4πr²
4π[(r + 7)² − r²] = 4312
4π(r² + 14r + 49 − r²) = 4312
4π(14r + 49) = 4312
56π(r + 3.5) = 4312
56 × 22/7 (r + 3.5) = 4312
176(r + 3.5) = 4312
r + 3.5 = 24.5
r = 21
V = (4/3)πr³
= (4/3) × 22/7 × 21³
= (4/3) × 22/7 × 9261 = 38808
Volume of the original sphere = 38808 cm³