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Homework Statement
Ok this is from a summer assignment that I had for calculus yet it's not calculus but it was graded by my calculus teacher so maybe there's something she knows that I don't from a calculus standpoint that allowed her to mark me wrong for this so here we go...
Write a function for the surface area of an open box with a square base of side x and height y whose surface area is 100 square feet.
Now strictly speaking I always thought that surface area was just that, area exposed to the surface of an object... I always thought that the assumption was that when not specified you just find the total area exposed to the surface, i.e. you don't subtract out the surface area that might be on the ground or what not because this is not a given, for example I remember like in other very simple math classes when we were asked to find the surface area of a sphere you would just use some formula... you didn't use calculus or anything to take out the area that is on the floor and is strictly speaking not exposed to the surface...
so in this case I found the total surface area of a floating box just like you would a sphere when not told... even if you were to assume that it was on the ground with the given information you don't know which side of the box is on the floor? Is it on the floor with it's square base touching the floor or maybe one of the longer rectangular sides? Or maybe it's on the floor and up against a wall in which case you would take out even more area that is not technically speaking exposed to the surface
So am I justified in find the area of a floating OPEN box? I thought so as if she wanted us to assume it was on the floor she would clearly have to give us more information as I just explained... plus like in the 9th grade geometry when finding spheres you didn't take out the area that wasn't exposed to the surface...
Well that was my logic...
so anyways for my equation I got
2x^2 + 8xy = 100 ft^2
then I wrote it in equation form
-x/4 + (25 ft^2)/2 = y
and she marked it wrong I don't see how or why
ok so the square base has a area of just x^2 but sense you got to count the bottom it's x^2 + x^2 or simply 2x^2 then there are 4 side panels of the box who have area xy but sense it's open you have to count it 8 times or simply 8xy then I set it equal to 100 ft^2 and then solved for y to make it a function
and she marked it wrong why? Is my equation wrong or what?