### Home > CALC > Chapter 1 > Lesson 1.4.2 > Problem1-152

1-152.

The shaded region below represents a quarter circle combined with a right triangle "flag."

1. Imagine rotating this flag about its "pole" and describe the resulting three-dimensional figure. Draw a picture of this figure on your paper. To help you visualize this, use the .

2. 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 $30° − 60° − 90°$ triangles.

The volume of a sphere is $\frac{4}{3}\pi r^{3}$, so the volume of half a sphere would be half of that. The volume for a cone is $\frac{1}{3}\pi r^{2}h$.

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