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Question

A cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic mere per hour. Then the depth of the wheat is increasing at the rate of (A) 1 m/h (B) 0.1 m/h (C) 1.1 m/h (D) 0.5 m/h

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Solution

The radius of the tank is 10m , and the rate of filling the tank is 314cubicmeterperhour .

Let the height of the cylindrical tank be h.

The volume of the tank is,

V=π× r 2 ×h =π ( 10 ) 2 h =100πh To find the rate of change of the volume, differentiate the above equation with respect to time.

dV dt =100π dh dt The tank is being filled by wheat at the rate of 314cubicmeterperhour . This is the rate of change of volume.

314=100π dh dt dh dt = 314 100×3.14 [ Takeπ=3.14 ] dh dt = 314 314 dh dt =1 Hence, the depth is increasing at a rate of 1m/h .

Thus, the correct option is (A).


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