CPM Homework Help : CALC Problem 5-109

A flag is formed by the region bounded by $y ≤ x + 3$ , $y ≤ −2x + 12$ , and the $x$ -axis. Find the volume of the solid formed by rotating the flag about the $x$ -axis.

Hint:

Sketch the graph and outline the flag. Notice that the resultant volume will be two cones each with radius $6$ , but different heights.

Answer:

$V = 108π$ units^{$^3$}