Question

A cylindrical vessel of radius $0.5m$ 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/ minute
• B. $2$ m/ minute
• C. $5$ m/ minute
• D. $1.25$ m/ minute

Answer 1

Answer: (A)

$1$ m/ minute

$V=\pi .r^2.h$
$\frac{dV}{dt}$
$=\pi .r^2.\frac{dh}{dt}$
$0.25\pi .=\pi .(0.5{)}^2.\frac{dh}{dt}$
Or
$0.25=\frac{1}{4}.\frac{dh}{dt}$
$1=\frac{dh}{dt}$
Hence the surface is rising at $1m/min$.