What is the 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 = 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

For finding the volume, first of all you need to find the area of square.

so you need the side of square , in this case side square is Y = 4 - X

Graph y+x = 4 and choose one point on the line the order pair of this point is (X,4-X)

area = (4 -X)^2

V = ∫area dx bounded x=0 t0 x = 4 ( x = 4 is x-int y +x =4)

V = ∫(4-X)^2 dx

V = -1/3 (4-x)^3

V = -1/3(0) + 1/3(4-0)^3

V = 64/3

I hope it is useful,

Minoo