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Volume of a solid of revolution?
I need to find the volume of a solid of revolution in two different ways and show that they are the same:
Find the volume of the solid of revolution bounded by:
y = x^3
x = 0
x = 2
rotated about the x-axis.
1) using the disk method
2) using the cylindrical shell method
1 Answer
- troutfisherLv 56 years ago
disk method" width of disk = dx, radius = y = x^3, volume element = pi x^6 dx
now you just integrate from 0 to 2
a cylindrical shell has a circumference of 2 pi y , a thickness of dy , and a height of
2 - x = 2 - y^1/3
so the volume element is 2 pi y (2 - y^1/3) dy
you integrate from y = 0 to y = 2^3 = 8
