Help with volume

Question

The base of a solid in the first quadrant of the xy plane is a right triangle bounded by the coordinate axes and the line x + y = 6. Cross sections of the solid perpendicular to the base are squares. What is the volume, in cubic units, of the solid?

Options:

1. 36
2. 18
3. 108
4. 72

Answer 1

Cheyanna, Sam has computed the area of the base of the solid. But to get the volume, we have to look at the description of the cross-sections.

Imagine the cross section at the x-z plane, X = 0. We are told It is a square, so it must be 6x6. Now move this plane over to x = 1, this square must be a 5x5. This continues until x= 6, when the square is 0x0.

so we want the integral of x², from 0 to 6

That is (x³/3 at x = 6 ) - (x³/3 at x= 0), which is 6³/3 = 216/3 = 72.

Answer number 4

Answer 2

The volume is 6*6/2=18. This triangle is a 45, 45, 90.