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 yaxes. When R is rotated about the xaxis, what is the volume of the
resulting solid? What is the volume of the solid generated by rotating R about
the yaxis?

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
Answer This Question
Related Questions
 Calculus  Let R be the region bounded by the xaxis, x = 5 and the curve y = x...
 Calc  The region bounded by y=2.5x^2 and y=4x is to be rotated about both axes ...
 Calculus  The region in the first quadrant bounded by y=6x^2 , 2x+y=8, and the ...
 Cal 2  The region bounded by y=3/x, y=0, x=3, and x=5 is rotated about the x...
 Cal 2  The region bounded by y=3x, y=0, x=3, and x=5 is rotated about the x...
 Calculus  Integrals  The region bounded by y=x^2, x=y^2 is rotated about the ...
 Math  Calculus  The region in the first quadrant bounded by y=6x^2 , 2x+y=8, ...
 Calculus  We're learning disks, shells, and cylinders in school but we have a ...
 Calculus  We're learning disks, shells, and cylinders in school but we have a ...
 Math  The region bounded by the given curves is rotated about the specified ...
More Related Questions