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

1-152.

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

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 1-152 eTool (Desmos).

Find the volume of the rotated flag.

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

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.