1. The problem statement, all variables and given/known data Here is the question along with the solution and sketch. I think the sketch is wrong because the projection in the xy plane shows a rectangular box. I don't think it is a rectangular box because you can solve for an equation relating x and y. You know that y = 1-z and x = 1-z^2, so you can solve for some equation with x and y by eliminated z. Which gets you x = -(y-1)^2 + 1 for the relationship in the xy plane and it is clearly not a rectangle...?