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/h  (B) 0.1 m/h  (C) 1.1 m/h  (D) 0.5 m/h

Solution:

Let r be the radius of the cylinder

Then, volume (V) of the cylinder is given by,

V = π r²h

= π (10)²h

V = 100 π h

Differentiating with respect to time (t), we have:

dV/dt = 100 π dh/dt

The tank is being filled with wheat at the rate of 314 m³/h

dV / dt = 314 m³/h

Thus, we have:

100 π dh/dt

= 314

dh / dt = 314 / 100(3.14)

= 1

Hence, the depth of wheat is increasing at the rate of 1 m/h.

Thus, the correct option is A

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NCERT Solutions Class 12 Maths - Chapter 6 Exercise ME Question 19

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/h (B) 0.1 m/h (C) 1.1 m/h (D) 0.5 m/h

Summary:

Given that a cylindrical tank of radius 10 m is being filled with wheat at the rate of 314 cubic metre per hour. The depth of wheat is increasing at the rate of 1 m/h. Thus, the correct option is A