The area enclosed between $y=x^2+2$ and $y=3$ is revolved about the horizontal line $y=3$ to form a solid. Calculate the volume. (Hint: Disks)
The only part that i'm confused on is how to calculate the radius. could someone explain how I would go about this?
So the radius of each disk is the distance between $y=3$ and $y=x^2+2$, or $1-x^2$.
For the radius, it is just the distance between the curves, so subtract :)
You are integrating between intersections, or $-1$ and $1$.
So, you have $\displaystyle π\int_{-1}^{1}(1-x^2)^2\,dx$.
Remember simply, that you are stacking circles on each other, you just need to know the radius, and apply $πr^2$. And as you stack each of the circles, you get an integral :)
P.S., this is not required, but if you notice that the solid formed will be symmetrical if divided by the plane $x=0$, you can rewrite the integral to $\displaystyle 2π\int_{0}^{1}(1-x^2)^2\,dx$.
This will make subtraction simpler if you need to do this by hand.