# The function that models the height of a cone in terms of its radius r whose volume is 100 in 3 .

### Precalculus: Mathematics for Calcu...

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

### 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 100 in3 .

Expert Solution

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 .

### Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!