Posted by nicko on Monday, January 3, 2011 at 6:16am.
find the volume formed by revolving the parabola y=4x^2 in the first quadrant:
a.) about x=0
b.) about x=2

calculus  Reiny, Monday, January 3, 2011 at 9:33am
a)
after making the diagram, take horizontal discs, so
volume = π[integral] x^2 dy from 0 to 4
= π[integral](4y)dy from 0 to 4
= π [4y  y^2/2] from 0 to 4
= π( 16  8  0) = 8π
b) since you only want to rotate the part in the first quadrant, look at your diagram.
I would find the volume of the cylinder with radius 2 and height of 4, the "hollow out" the part contained by y = 4x^2, x=2 and y=4
we need the radius or the x of that part, which is 2  √(4y)
but we will need x^2 which is
4  2√(4y) + 4y
= 8  y  2(4y)^(1/2)
this will have to be integrated to give
8y  y^2/2 + (4/3)(4y)^(3/2)
see if you can finish it from here.
Answer This Question
Related Questions
 Calculus  Find the volume of the solid generated by revolving the region in the...
 calculus  Let R be the region in the first quadrant that is enclosed by the ...
 Calculus  Compute the volume of the solid formed by revolving the fourth ...
 Calculus  Compute the volume of the solid formed by revolving the fourth ...
 calculus  1. Let R be the region in the first quadrant enclosed by the graphs ...
 Calculus  1. Use cylindrical shells to compute the volume of the solid formed ...
 Calculus  The region R is in the first quadrant and bounded by the xaxis, the ...
 Can no one help?!  1. Use cylindrical shells to compute the volume of the solid...
 Calculus  Find the volume of the solid generated by revolving the following ...
 MATH  Find the volumes of the solids generated by revolving the region in the ...
More Related Questions