Answered: An oil spill is the shape of a thin…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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An oil spill is the shape of a thin cylinder which is constantly 2 cm thick and is expanding. The volume of the spill is increasing by 30 cm^3 /sec. How fast is the radius increasing when the radius of the spill is 200 cm? The volume of a cylinder of heigh h and radius r is V= pi *r^2 *h

Solution = _________

Expert Solution

Step 1

Let r and h, in cm be the radius and height of cylinder at any time t . Let V cm^3 be the volume of cylinder at any time t. Height of cylinder is constantly 2 cm, that is h=2cm.

Since, volume of the spill is increasing by 30 cm^3 /sec.

Therefore,

Step 2

Now, Volume of cylinder is

Substitute h=2 cm

When r=200 cm

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