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प्रश्न
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
पर्याय
1 m/minute
2 m/minute
5 m/minute
1.25 m/minute
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उत्तर
1 m/minute
\[\text { Le tr be the radius,h be the height and V be the volume of the cylindrical vessel at any time t.Then, }\]
\[V = \pi r^2 h\]
\[ \Rightarrow \frac{dV}{dt} = \pi r^2 \frac{dh}{dt}\]
\[ \Rightarrow \frac{dh}{dt} = \frac{1}{\pi r^2}\frac{dV}{dt}\]
\[ \Rightarrow \frac{dh}{dt} = \frac{0 . 25\pi}{\pi \left( 0 . 5 \right)^2}\]
\[ \Rightarrow \frac{dh}{dt} = \frac{0 . 25}{0 . 25}\]
\[ \Rightarrow \frac{dh}{dt} = 1 m/\min\]
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