Calculus 3 Section 15.7

MATH 2531: SECTION 15.7 WRITTEN ASSIGNMENT This exercise is adapted from a problem from the textbook. The image is taken from the textbook as well. Consider "the solid between the sphere p = cos() and the hemisphere p = 2, = 2 0" (p. 951). IN p = cos b p=2 1. Recall that the volume of a sphere is mrs. Using basic geometry, find the volume of this solid by considering this solid carefully. Notice that this shape is more complicated than just a hemisphere. 2. Express the volume of the solid as a triple integral in spherical coordinates. 3. Evaluate the integral you obtained in #2. Confirm that the answer you obtained matches the value you found in #1