Question

Sculpture is in the shape of a cone. The sum of its radius and height is 30 in. Use a graphing calculator to find the radius, to the nearest inch, that gives the largest possible volume for the sculpture.

A 10 in.

B 15 in.

C 20 in.

D 30 in.

Answer 1

Option C.
`r=20\ in`

Explanation:

we know that

The volume of a cone is equal to

`V=(1)/(3)\pi r^(2)h` ------> equation A

In this problem we have

`r+h=30`

`h=30-r` -----> equation B

substitute equation B in equation A

`V=(1)/(3)\pi r^(2)(30-r)`

using a graphing tool

the largest possible volume for the sculpture is for
`r=20\ in`

see the attached figure