Question

find the volume of the solid formed by revolving the region bounded by the graphs of y=x^3,y=1, and x=2 about the x-axis using the disk method. 9 express the answer in terms of pie)

i got the answer to be 3/5 pie but im not sure if is right. i used the formula V=(pie)(r)^2W

Answer 1

V=πr²W applies to the volume of a uniform solid cylinder of length W and radius r.

The volume in question is very much like a hollow truncated cone.

Since y=x^3 and y=1 intersect at (1,1), the volume of the solid starts at x=1.
The elemental disk has a volume of
2π(x^3-1)dx
So integrating from x=1 to 2 gives you the volume of revolution.
I get 11π/2.
Check my thinking.