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1-152.

Pole figureThe shaded region at right 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. Calculate 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.

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