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Question

A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. Then the depth of the wheat is increasing at the rate of
(a) 1 m/hr
(b) 0.1 m/hr
(c) 1.1 m/hr
(d) 0.5 m/hr

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Solution

(a) 1 m/hr

Let r, h and V be the radius, height and volume of the cylinder at any time t. Then, V=πr2hdVdt=πr2dhdt314=3.14 × 102dhdtdhdt=314314dhdt=1 m/hr

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