Question

Terri’s Ice Cream Parlor makes gourmet ice cream cones. The volume of each cone is
8
cubic
inches. The height is 4 inches more than the radius of the cone’s opening.
a.) Write a polynomial function that represents the volume of the ice cream cone in terms of the radius
(the formula for the volume of a cone is
1 2
3
V r h  
).
b.) What are the possible values of
r
?
c.) Find the dimensions of the cone.

Answer 1

re-formatting the question so it's a little easier to read:

Terri’s Ice Cream Parlor makes gourmet ice cream cones. The volume of each cone is 8 cubic
inches. The height is 4 inches more than the radius of the cone’s opening.

a.) Write a polynomial function that represents the volume of the ice cream cone in terms of the radius (the formula for the volume of a cone is V = (1/3)pi * r^2 * h

b.) What are the possible values of r?

c) Find the dimensions of the cone.

Answer 2

a) "The height is 4 inches more than the radius of the cone’s opening."
therefore, h = r + 4

"The volume of each cone is 8 cubic inches"
therefore, V = 8

if you plug these into the volume formula, you'll have an equation in terms of r. solve for r.

Answer 3

b) once you've solved for r, consider which of your r-values is actually a viable solution to this problem. remember, r stands for the radius of the cone so it must be a positive number

c) you already have r. since h = r + 4, simply add 4 to the radius to get the height. radius and height are the dimensions you'll report.