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**HallsofIvy** You don't need to use Calculus at all. The line y= 3x, from x= 0 to 1, rotated around the x-axis, gives a cone with "height" 1 and base radius 3(1)= 3. The lline y= 2x, from x= 0 to 1, rotated around the x-axis, cone with "height" 1 and base radius 2(1)= 2. Look up the formula for volume of a cone, find each of those areas, and subtract the inner cone from the outer cone.

If you really **want** to use Calculus, you can use the "washer method". The a vertical line between those two lines, rotated around the x-axis will form a "washer", a disk with a hole in it. Its area is the are between the two cirles, $\displaystyle \pi(3x)^2- \pi(2x)^2$. Its thickness, dx, gives volume $\displaystyle \pi(9- 4)x^2 dx= 5\pi x^2 dx$. Integrate that from x= 0 to 1.