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he volume of oil in a cylindrical container is increasing at a rate of cubic inches per second. the height of the cylinder is approximately ten times the radius. at what rate is the height of the oil changing when the oil is inches high? (hint: the formula for the volume of a cylinder is

Sagot :

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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