If the radius of a spherical balloon is increasing at the rate of 5 inch per minute, then the rate at which the volume increases (in cube inches per minute) when the radius is 10 inches is

Question

If the radius of a spherical balloon is increasing at the rate of 5 inch per minute, then the rate at which the volume increases (in cube inches per minute) when the radius is 10 inches is, 100 π, 1000 π, 2000 π, 25000 π

MARKS App · Accepted Answer

Given, d r d t = 5 inch/minute r = 10 inches Volume of spherical balloon is V = 4 3 π r 3 Differentiating w. r. t. t d d t V = d d t 4 3 πr 3 d V d t = 4 3 × 3 πr 2 d r d t d V d t = 4 π × 100 × 5 d V d t = 2000 π cubic inches per minute

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