CPM Homework Help : CALC Problem 2-39

Calculate the volume of the solid formed by rotating the flag bound by the $x$ - and $y$ -axes and $y = \sqrt { 9 - x ^ { 2 } }$ , in the first quadrant, about the $y$ -axis.

Hint 1:

Hint 2:

The area contained in the first quadrant is under a quarter-circle.

Hint 3:

The flag will be rotated about the $y$ -axis. This will result in the same volume as rotating about the $x$ -axis.

Hint 4:

The resultant 3D figure will be a half-sphere.