Find Volume in cubic units of the solid

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 = 4. Cross sections of the solid perpendicular to the base are squares. What is the volume, in cubic units, of the solid?

Question options:

1)	8
2)
3)
4)

Answer 1

If we take point with x-coordinate x then section perpendicular to base and paralle to line x + y = 4 is square with side xsqrt2. Because area of section is (xsqrt2)²= 2x².

Because volume of this object V = ∫₀⁴2x²dx = 2x³/3₀⁴ = 2(4³)/3 = 128/3.

Answer is 4). .