BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071
BuyFind

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2, Problem 18P
To determine

To find: The function that models the height of a cone in terms of its radius r whose volume is 100in3 .

Expert Solution

Answer to Problem 18P

The function that models the height of given cone is h(r)=300πr2 .

Explanation of Solution

The volume of the cone is,

V=13πr2h

Substitute 100 for V in above equation and get h in terms of r.

100=13πr2h

Multiply both sides of above equation by 3.

(3)100=(3)13πr2h300=πr2h

Divide the above equation by πr2

300πr2=h

Thus, the function that models the height of cone is h(r)=300πr2,r>0 .

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