CPM Homework Help : APCALC Problem 3-181

Calculate the volume of the solid created when the semi-circular flag at right is rotated about the pole. Describe the rotated solid.

Hint 1:

This flag will look like a sphere with a cylindrical hole removed from its center.

Hint 2:

$\text{volume} = \text{sphere} − \text{cylinder}$

$=\frac{4}{3}\pi r^{3}-\pi r^{2}h$

Hint 3:

Use the Pythagorean Theorem to compute the radius of the sphere.

Horizontal segment, with diameter of semicircle on the right 3 fourths of the segment, rectangle inscribed in semicircle, top edge labeled 8, right edge labeled 6, regions outside of rectangle, but inside semicircle are shaded.