CPM Homework Help : APCALC Problem 2-101

The region bounded by $y = -x + 6$ and the coordinate axes is rotated about the $y$ -axis. Calculate the volume of the resulting solid.

Hint 1:

Sketch the region so you can visualize the flag.

Hint 2:

The axis of rotation (the pole) is the $y$ -axis.

Hint 3:

The resulting solid will be a cone.

$V= \frac{1}{3}\pi r^{2}h$

Hint 4:

Which axis contains the radius $(r)$ and which contains the height $(h)$ ?