Find the volume of a described solid

[Physicsisfun2005]

I don't have the answers in the back of my book and I really want to know if i did this correctly since its graded. the Problem is: Let the region bounded by $$x^2+y^2=9$$ be the base of a solid. Find the Volume if cross sections taken perpendicular to the base are isosceles right triangles.
i know a triangle is $$.5bh$$ and the base of it will be $$\sqrt{9-x^2}$$ so for volume the final answer is $$\pi\int 4.5-.5x^2 dx$$ with the limits from -3 to 3 and i get $$18\pi$$ for volume.....is this right?

 

[wais]

Your calculation looks correct to me! To double check, you can graph the region and the cross sections to make sure they match up with your calculations. Also, it never hurts to double check your integration and make sure you didn't make any mistakes. But overall, it looks like you have the right approach and answer. Great job!