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

Options

A. 1 m/h
B. `0.1 m//h`
C. ` 1.1 m//h`
D. `0.5 m//h`

Answer

A

Explanation

Let at nay time 't' hour, the depth of wheat in cylinder be h metre and volume of wheat be `V m^(3)`.
`:. V = pi r^(2) h = pi (10)^(2) h = 100pi h`
` rArr (dV)/(dt) = 100pi (dh)/(dt) rArr 314 = 100pi (dh)/(dt) ("given",(dV)/(dt) = 314)`
` rArr (dh)/(dt) = (314)/(100 (3.14)= 1 ` m/hr
` :. ` The depth of wheat is increasing at the rate of 1 m/hr.