Chapter 11.4, Problem 93E

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Chapter
Section

### Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

# Budget Overruns The Pentagon is planning to build a new spherical satellite. As is typical in these cases, the specifications keep changing, so the size of the satellite keeps growing. In fact, the radius of the planned satellite is growing 0.5 feet per week. Its cost will be $1,000 per cubic foot. At the point when the plans call for a satellite 10 feet in radius, how fast is the cost growing? (The volume of a solid sphere of radius r is V = 4 3 π r 3 .) To determine To calculate: The rate at which the cost is growing when the plans call for the satellite 10 feet if the pentagon is planning to build a new spherical satellite, as it is typical in cases, the specifications keep changes and the size of the satellite keeps growing and the radius of the planned satellite is growing 0.5 feet per week. Also, its cost will be$1,000 per cubic foot.

Explanation

Given Information:

The pentagon is planning to build a new spherical satellite, as it is typical in cases, the specifications keep changes and the size of the satellite keeps growing and the radius of the planned satellite is growing 0.5 feet per week. Also, its cost will be \$1,000 per cubic foot. Area of a disc of radius r is V=43πr3

Formula used:

Derivative of function f(x)=(u)n using chain rule is f'(x)=ddx(u)n=nun1dudx, where u is the function of x and dudx is unspecified.

Calculation:

Consider the function, V=43πr3

Evaluate the derivative of the function by applying the chain rule,

dVdt=ddt(43πr3)=43(3)πr2drdt=4πr2drdt

Substitute r=10 and drdt=0

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