CPM Homework Banner

Home > CALC > Chapter 1 > Lesson 1.4.2 > Problem 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 triangles.

    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