Posted by **MAM** on Tuesday, January 24, 2012 at 9:43pm.

Use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the y-axis.

y = 6x

y = 18

x = 0

- calculus -
**Steve**, Wednesday, January 25, 2012 at 12:57pm
V = Int(2pi*r*h dx)[0,3]

where

r = x

h = 18-y

V = 2pi*Int(x*(18-6x) dx)[0,3]

= 2pi * Int(18x - 6x^2 dx)[0,3]

= 2pi*(9x^2 - 2x^3)[0,3]

= 2pi*(27-18)

= 18pi

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