PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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# Solution for 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 (A) 1 M/Minute (B) 2 M/Minute (C) 5 M/Minute - PUC Karnataka Science Class 12 - Mathematics

#### 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
(a) 1 m/minute
(b) 2 m/minute
(c) 5 m/minute
(d) 1.25 m/minute

#### Solution

(a) 1 m/minute

$\text { Letrbe the radius,hbe the height andVbe the volume of the cylindrical vessel at any timet.Then, }$

$V = \pi r^2 h$

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

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

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

$\Rightarrow \frac{dh}{dt} = \frac{0 . 25}{0 . 25}$

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

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Solution 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 (A) 1 M/Minute (B) 2 M/Minute (C) 5 M/Minute Concept: Rate of Change of Bodies Or Quantities.
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