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

1-152.
1. The shaded region below represents a quarter circle combined with a right triangle "flag." Homework Help ✎

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 1-152 eTool (Desmos).

2. 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.

$\text{The volume of a sphere is }\frac{4}{3}\pi r^{3},\text{ so the volume of half a}$

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