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An accident at an oil drilling platform is causing a circular oil slick which is harmful to marine life. The slick is 0.08 foot thick, and when the radius of the slick is 150 feet, the radius is increasing at the rate of 0.5 foot per minute. At what rate (in cubic feet per minute) is oil flowing from the site of the accident?

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bayosanuade

Answer:  37.7 feet per minute

Step-by-step explanation:

Given:

radius = 150

[tex]\frac{dr}{dt}[/tex] = 0.5

h = 0.08

To calculate : [tex]\frac{dv}{dt}[/tex]

Volume of cylinder is given as:

V = [tex]\pi r^{2}h[/tex]

[tex]\frac{dv}{dr}[/tex] = [tex]2\pi rh[/tex]

[tex]\frac{dv}{dt}=\frac{dv}{dr} X \frac{dr}{dt}[/tex]

[tex]\frac{dv}{dt}[/tex] = [tex]2\pi rh[/tex] ×0.5

[tex]\frac{dv}{dt}[/tex] = 2 X 22/7 X 150 X 0.08 X 0 .5

[tex]\frac{dv}{dt}[/tex] = 37.7 feet/mi

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