Have a think about the shape that is made when the line is rotated through around the x-axis. There is a formula for calculating the volume of such a shape (hint: , where h is height and r is radius).
Having a bit of trouble with this one. Can anyone help me out?
Q. The given diagram (see attachment) shows the line [tex]y=2x[tex]. Find the volume generated when this line is rotated about the x-axis from to
Attempt: If , the height of the generated volume is also 3.
For , . Thus, the height of the volume generated is 6.
Ans.: (From text book):