Determining the Surface Area of a Solid of Revolution
Key Questions

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 + (y3/2)^2 = 9/4# You recognize a circle of radius
#3/2# . The area is#pi (3/2)^2 = 9 pi/ 4# . 
If a surface is obtained by rotating about the xaxis the polar curve
#r=r(theta)# from#theta=theta_1# to#theta_2# , then its surface area A can by found by#A=2pi int_{theta_1}^{theta_2}r(theta)sin theta sqrt{r^2+[r'(theta)]^2} d theta# .
I hope that this was helpful.
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