How do I find the surface area of the solid defined by revolving #r = 3sin(theta)# about the polar axis?

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Answer 1 · 2015-02-24T00:17:56

Write :

#r = 3 sin(theta)#

#r = 3y/r# because #y=r sin(t)#

#r^2 = 3y#

#x^2 + y^2 = 3y# because #r = sqrt(x^2+y^2)#.

#x^2 + (y-3/2)^2 = 9/4#

You recognize a circle of radius #3/2#. The area is #pi (3/2)^2 = 9 pi/ 4#.