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..

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?

Answer 1

Triangle area = 6(6)/2 = 18

square cross sections are vertical slices varying up to 3sqr2, the hypotenuse of the triangle base

for each square cross section x=y and z=xsqr2 = height. triangular area = x^2/2 for each cross section

use the vertical axis as z for height

integrate x^2/2(x)sqr2 = (sqr2)/2)(x^3) evaluated from 0 to 3

= sqr2 x^4/8= (81/8)sqr2 = about 14.32 cubic units

It's hard to visualize the cross sections or how the problem intends them. But maybe 14.32 is right.