A spherical balloon is expanding. If the radius is increasing at the rate of $ 2 \mathrm{~cm} / \mathrm{min} $ the rate at which the volume increases (in cubic centimeters per minute) when the radius is $ 5 \mathrm{~cm} $, is

Question

A spherical balloon is expanding. If the radius is increasing at the rate of $ 2 \mathrm{~cm} / \mathrm{min} $ the rate at which the volume increases (in cubic centimeters per minute) when the radius is $ 5 \mathrm{~cm} $, is, $ 10 \pi $, $ 100 \pi $, $ 200 \pi $, $ 50 \pi $

MARKS App · Accepted Answer

As, volume of sphere V = 4 3 π r 3 ⇒ d V d t = 4 π r 2 d r d t = 4 π r 2 . ( 2 ) [ ∵ d r d t = 2 ] ⇒ d V d t = 4 π . 25 . 2 = 200 π

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