   Chapter 11.4, Problem 30E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Water purification Assume that water is being purified by causing it to flow through a conical filter that has a height of 15 in. and a radius of 5 in. If the depth of the water is decreasing at a rate of 1 in. per minute when the depth is 6 in., at what rate is the volume of water flowing out of the filter at this instant?

To determine

To calculate: The rate of change of volume of water flowing out of the filter at an instant when the depth is 6 in. if the water is flowing through a conical filter that has a height of 15 in. and a radius of 5 in. and the depth of water is decreasing at a rate of 1 in. per minute.

Explanation

Given Information:

The water is flowing through a conical filter that has a height of 15 in. and a radius of 5 in. and the depth of water is decreasing at a rate of 1 in. per minute when the depth is 6 in.

Formula used:

The volume of a cone of radius r and height h is given by,

V=13πr2h

Calculation:

As it is provided that a conical filter that has a height of 15 in. and a radius of 5 in.

So, the cone will be,

Now, the volume of a cone of radius r and height h is given by,

V=13πr2h

Since, rh=515

Then,

13h=r

Take, differentiation with respect to t as,

13dhdt=drdt

Substitute 1 for dhdt in the equation 13dhdt=drdt as,

13(1)=drdt13=drdt

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