The shaded region below represents a quarter circle combined with a right triangle "flag."
Find the volume of the rotated flag.
Sum together the volumes of the cone and the half-sphere. Note that the radius is obtained by using the trigonometry rule for
The volume of a sphere is
, so the volume of half a sphere would be half of that. The volume for a cone is .
Use the eTool below to visualize the flag.
Click the link at right for the full version of the eTool: Calc 1-152 HW eTool