Question

R is bounded by the x axis, the y axis, and the line x=3 - y

Answer 1

sure looks like a triangle to me.

Answer 2

The area of the region is pretty simple since it's a triangle. If you graph it, it has endpoints at (3,0) and (0,3), telling us the dimensions of the triangle. Thus, the area of the region is (3*3)/2 = 9/2 = 4.5 square units

You don't give a revolution axis for the volume, so I'm assuming you just wanted the area of the region.

Answer 3

Could be x axis, could be y axis, no difference. However should say particularly if the axis is at some odd angle :)

Answer 4

But it also might not be either axis! Perhaps the lines x=5 or y=4 for instance. That volume would change.