Water is being poured at the rate of 36 m^3 | vedclass

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Question

(A) The volume $V$ of a cylinder is given by the formula $V = \pi r^2 h$,where $r$ is the radius of the base and $h$ is the height of the water level.

Vedclass · Accepted Answer

$\frac{4}{\pi} \ m / min$

Vedclass · Answer

(A) The volume $V$ of a cylinder is given by the formula $V = \pi r^2 h$,where $r$ is the radius of the base and $h$ is the height of the water level.Given that the radius $r = 3 \ m$ is constant,we differentiate the volume with respect to time $t$:$\frac{dV}{dt} = \pi r^2 \frac{dh}{dt}$We are given the rate of change of volume $\frac{dV}{dt} = 36 \ m^3 / min$.Substituting the known values into the equation:$36 = \pi (3)^2 \frac{dh}{dt}$$36 = 9 \pi \frac{dh}{dt}$$\frac{dh}{dt} = \frac{36}{9 \pi} = \frac{4}{\pi} \ m / min$Thus,the water level is rising at the rate of $\frac{4}{\pi} \ m / min$.

Water is being poured at the rate of $36 \ m^3 / min$ into a cylindrical vessel,whose circular base has a radius of $3 \ m$. Then the water level in the cylinder is rising at the rate of:

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