Published by:
CGP EDU Academic Team
Published on: August 14, 2026
A spherical balloon is filled with 4500 π cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72 π cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is :
A
B
C
D
Text Solution
Verified by ExpertsThe correct answer is:
C
V = 
π r 3 4500 π = 
= 4 π r 2 
45 × 25 × 3 = r 3
r = 15 m
after 49 miN
= (4500 – 49.72) π
=972 π m 3
972 π = π r 3
r 3 = 3×243
= 3× 3 5
r = 9
72 π = 4 π × 9 × 9 
= 
r 3 = 3×243
= 3× 3 5
r = 9
72 π = 4 π × 9 × 9 
⇒ 
= 
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