Consider a circular cone of radius 3 and height 5, which we view horizontally as pictured below. Our goal in this activity is to use a definite integral to determine the volume of the cone.

** (a) ** Find a formula for the linear function

** (b) ** For the representative slice of thickness

** (c) ** What is the volume

** (d) ** What definite integral

What is the exact value of this definite integral?

** (e) ** Compare the result of your work in (d) to the volume of the cone that comes from using the formula

You can earn partial credit on this problem.