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The shaded region at right 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.

  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 triangles.

Adjacent angles forming a linear pair, with line segment labeled pole, shaded left angle, labeled 30 degrees, top ray of angle labeled 10.

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