Answer :
Height of oil changes at the rate of [tex]\frac{200}{49\pi}[/tex] inch\sec
What is rate of change?
Suppose there is a function and there are two quantities. If one quantity of a function changes, the rate at which other quantity of the function changes is called rate of change of a function.
Here rate of change of height has been calculated
Let the radius be r inch and height of the cylinder be 10 inch
It is given
h = 10r
Volume of cylinder (V) = [tex]\pi r^2 h[/tex]
= [tex]\pi (\frac{1}{10}h)^2h\\\frac{1}{100}\pi h^3[/tex]
[tex]\frac{dV}{dt} = \frac{d}{dt}\frac{1}{100}\pi h^3\\[/tex]
[tex]= \frac{3}{100}\pi h^2\frac{dh}{dt}[/tex]
[tex]150 = \frac{3}{100}\times \pi \times35^2 \times \frac{dh}{dt}\\\frac{dV}{dt} = \frac{147}{4}\pi \frac{dh}{dt}\\150 = \frac{147}{4}\pi \frac{dh}{dt}\\\frac{dh}{dt} = \frac{600}{147\pi}\\\frac{dh}{dt} = \frac{200}{49\pi}[/tex]
Height of oil changes at the rate of [tex]\frac{200}{49\pi}[/tex] inch\sec
To learn more about rate of change, refer to the link-
https://brainly.com/question/24313700
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