UCI
MATH 2E -
Quiz 5
Unformatted text preview:
View Full Document
Math 2E 44275 Spring 2014 Quiz 5 5 22 14 Name Print ID Number Show all of your work Partial credit will be given 1 10 points Find the area of the part of the sphere that lies inside the cylinder x2 y2 9 x2 y2 z2 16 Solution The cylinder encloses separate portions of the sphere in the upper and lower halves The top half of the sphere is z f x y p16 x2 y2 and D is given by x y x2 y2 9 The surface area of the upper enclosed portion is A ZZ ZZ x vuut1 r 0 p16 r2 3 2 p16 x2 y2 Z 3 Z 2 0 2 4 16 x2 y2 dA 16 0 0 D D 4 2 p16 x2 y2 y 2 dA Z 2 s ZZ 1 x2 y2 Z 3 D r 16 r2 dr 16 x2 y2 dA 4 16 r2 16 9 rdrd 4 d 16 0 8 4 0 0 7 The lower portion of the sphere enclosed by the cylinder has identical shape so the total area is 2A 16 4 7
View Full Document
Unlocking...