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 = 2. Cross sections of the solid perpendicular to the base are squares. What is the volume, in cubic units, of the solid?
Steve you’re so damn annoying bro don’t answer the questions if ur gonna keep on !@#$%^&ing
Actually Steve is correct, it's the question that's wrong here. Normally, the answer should have been 8/3 assuming you had only found the area on just one half of the figure but Steve multiplied this by 2 to get the entire figure (since there are squares on both sides given that the left and right directions are perpendicular to the base). Hope this makes sense
Mathematics.
that is all the information given
How are the cross-sections oriented?
perp. to an axis, parallel to x+y=2, or some other way?
so whats the answer
well, it ain't enough. If the cross-sections are perpendicular to the x- (or y-)axis, then each thin plate has base of width 2-x, so
v = ∫[0,2] (2-x)^2 dx = 8/3
If the cross-sections are parallel to the line x+y=2, then each thin slice has base √(x^2+y^2) = √(x^2+(2-x)^2), so
v = ∫[0,2] x^2+(2-x)^2 dx = 16/3