Volume of solids question (1 Viewer)

[MrKay]

Volume of solids of revolution

The area bounded by the parabola y =2x -x^2, the y-axis and the line y=1 is rotated about the x-axis. Find the volume generated.


So since it's asking about the revolution when that region is rotated about the x-axis, I set a=0 and b=1
and y^2= 4x^2-4x^3+x^4

so my formula ended up as V= pi [4x^3/3 - x^4 + x^5/5] b=1 on top and a=0 on bottom
= 8/15 pi

However, the answer in the textbook turned out to be different, giving something very confusing


Anyone have a solution as to how they got that extra pi to minus the pi already in the formula?

 

[pikachu975]

To find area bounded by the x axis you have to do the square area minus the area under the parabola. So to find the volume, you have to do volume of the rectangle rotated around the x axis (which forms a cylinder if you imagine it) minus the volume of the parabola area rotated about the x axis.

The volume of a cylinder is V = pi*r^2 *h
V = pi*1^2 * 1
= pi

So total V = pi - the integral you had.