See attachment -- I get 16/15
R is the region bounded below by y=x^2 and above by y=1. Suppose a solid has base R and the cross-sections of the solid perpendicular to the y-axis are squares. Find the volume of this solid.
I know the answer is 2 (I think), but can someone explain how to do this?
I also get 2. Since you want the cross-sections to be perpendicular to the y-axis, it's probably best to look at this as a function of y. So we have .
Because the length of the square goes from to , the side length of each square is . Thus the equation you want to integrate is:
and this does come out to 2.
Calculus26's math is right, but in his post he has the side lengths parallel to the y-axis, not perpendicular, and this changes the answer.