Question

A cylindrical vessel of radius 0.5 m is filled with oil at the rate of 0.25 π m³/minute. The rate at which the surface of the oil is rising, is

Options

• 1 m/minute

•  2 m/minute

•  5 m/minute

• 1.25 m/minute

Answer 1

1 m/minute

\[\text { Le tr be the radius,h be the height and V be the volume of the cylindrical vessel at any time t.Then, }\]

\[V = \pi r^2 h\]

\[ \Rightarrow \frac{dV}{dt} = \pi r^2 \frac{dh}{dt}\]

\[ \Rightarrow \frac{dh}{dt} = \frac{1}{\pi r^2}\frac{dV}{dt}\]

\[ \Rightarrow \frac{dh}{dt} = \frac{0 . 25\pi}{\pi \left( 0 . 5 \right)^2}\]

\[ \Rightarrow \frac{dh}{dt} = \frac{0 . 25}{0 . 25}\]

\[ \Rightarrow \frac{dh}{dt} = 1 m/\min\]