Question

A right circular cylinder has a diameter of 12 in and a height of 12 in. if water is flowing in at the rate of 4π in3 per minute, find the rate of change of the height when the height is 4 in?

Answer 1

The rate of change of the height is $\frac{1}{9}$ in/min.

What is a right circular cylinder?

A right circular cylinder is a cylinder that has a closed circular surface having two parallel bases on both the ends and whose elements are perpendicular to its base. It is also called a right cylinder.

Volume of the cylinder = $\pi r^{2}h$

Rate of change of height is  $\frac{dh}{dt}$ = ?

At any time t,

Volume, V =  $\pi r^{2}h$

Since r does not change with time, then r is a constant, so,

V =  $\pi (6)^{2}h$

V = $36\pi h$

Differentiate both sides with respect to time t,

$\frac{dV}{dt} = 36\pi \frac{dh}{dt}$ -------------(i)

Since $\frac{dV}{dt}$is given as 4$\pi$ cu.in. per min,

$4\pi = 36\pi \frac{dh}{dt}$

$\frac{dh}{dt} = \frac{4\pi }{36\pi }$

$\frac{dh}{dt} = \frac{1 }{9 }$ in/min.

Hence, The rate of change of the height is $\frac{1}{9}$ in/min.

To learn more about right circular cylinder from the given link:

brainly.com/question/2762448

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