# Calculus

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?

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1. How are the cross-sections oriented?

perp. to an axis, parallel to x+y=2, or some other way?

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2. that is all the information given

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3. 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

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4. Steve you’re so annoying bro don’t answer the questions if ur gonna keep on !@#\$%^&ing

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5. 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

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6. Mathematics.

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