Posted by **Macy** on Thursday, December 1, 2011 at 11:53am.

Let R be the square region bounded by y = 2, x = 2, and the

x and y-axes. When R is rotated about the x-axis, what is the volume of the

resulting solid? What is the volume of the solid generated by rotating R about

the y-axis?

- Calculus -
**Steve**, Thursday, December 1, 2011 at 12:49pm
first, since it's a square, it does not matter which side is used as the rotational axis.

geometrically, we have a cylinder of height=2, radius=2

v = pi * 2^2 * 2 = 8pi

Analytically,

v = Integral(pi y^2 dx)[0,2]

= Integral(4pi dx)[0,2]

= 4pi x[0,2]

= 8pi

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