Consider the volume of the region shown below, which shows a right circular cone with top radius 1 cm and height 5 cm. We have used the notation for .

figure showing a right-circular cone with the distance y measured up from its point to a slice of thickness Dy.

Write a Riemann sum for the volume, using the strip shown and the variable :
Riemann sum

Now write the integral that gives this volume:
and .

Finally, calculate the exact volume of the region, using your integral.
volume =
(include units)

You can earn partial credit on this problem.