A cylindrical vessel of radius 0.5 m is filled with oil at the rate of 0.25`pi``m^3``/`minute. The rate at which the surface of the oil is rising, is (a) 1 m/min.    (b) 2 m/min.   (c) 5 m/min.   (d) 1.25 m/min.

Options

A. 1 m / minute
B. 2 m / minute
C. 5 m / minute
D. 1.25 m / minute

Answer

A

Explanation

Let r be the radius, h be the height and V be the volume of the oil at time t. Then,
`V=pir^(2)h`
`impliesV=(pi)/(4)h" "[because r=0.5 m =(1)/(2)"(given)"]`
`implies (dV)/(dt)=(pi)/(4)(dh)/(dt)`
`implies 0.25 pi=(pi)/(4)xx(dh)/(dt) " "[because(dV)/(dt)=0.25 pi m^(3) "(given)"]`
`implies (dh)/(dt)=1m//"minute"`