Volume of solid bounded by cylinder and plane???

Question

find the volume of the solid in the first octant bounded by the cylinder z = 9 - y^2 and the plane x = 4 My answer was 56

Answer 1

I think you have a typo.  Z should be squared, or it won't be a cylinder.

z²+y²=9 is a circle with radius 3.  The first octant means you only take a quarter of the circle for cross-sectional area, then multiply by a height of 4 (bounded by x=4 on the top and x=0 on the bottom).

So the volume would be 4 times 1/4 the area of a circle of radius 3...or just πr² since the 4 and the 1/4 cancel each other.  

In other words, 56 is wrong.