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:

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5 0

2 years ago

Elvaluate the expression.<br>9!/3!<br>a) 3<br>b) 6<br>c) 60,480<br>d) 362,874

HACTEHA [7]

Answer:

c) 60,480

Step-by-step explanation:

9×8×7×6×5×4×3×2×1

3×2×1

Cancel same numbers in the numerator and denominator.

So you're going to have= 9×8×7×6×5×4 divided by 1

Which gives you, 60,480.

Hope this helped:) Mark me brainiest please.

4 0

3 years ago

A scientist recently submitted a paper to a leading scientific journal.

Reil [10]

The answer is B hope this helped

5 0

3 years ago

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