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 that is pictured above.

(b) For the representative slice of thickness that is located horizontally at a location (somewhere between and ), what is the radius of the representative slice? Note that the radius depends on the value of .

(c) What is the volume of the representative slice you found in (b)? (Use D as the value for )

(d) What definite integral will sum the volumes of the thin slices across the full horizontal span of the cone?

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.