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

Answer 1

Correct answer is A.

The volume of a cylinder, of radius r and height h, is defined as

V(r, h) =πr²h

Given that r = 10m, we get

V(h) = π × 10² × h = 100πh – (1)

Given that \(\frac{dV}{dt}=314\) m³/hr, we have to calculate \(\frac{dh}{dt}\)

Differentiating (1) with respect to t, we get

Substituting values and using π = 3.14, we get