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 ______.

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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 1 m/h. Explanation: Let the length of the cylindrical tank be h and the radius be r. volume of tank = $\pi$r2h = $\pi$ $\times$ 10 $\times$ 10 $\times$ h ...[∵ r = 10m] V = 100 $\pi$ h rate of change of volume (dV)/(dt) = 100 pi (dh)/(dt) ...(1) 314 = 100 pi (dh)/(dt) `therefore (dh)/(dt) = 314/(100 pi) = 314/(100 xx 3.14)` ... [∵ $\pi$ = 3.14] = 1 m3 / h

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