Page 37 - How To Solve Word Problems In Calculus

7. Since the boxhas a square base, its dimensions are x, x, and y.
2
V = x y.

y

x
y

x
x
x x

The surface area of the boxis the sum of the areas of its five sides.
Since the base of the boxis a square of side x and each of the four
2
sides is a rectangle x by y, S = x + 4xy.
Area Area of
of base 4 sides

x 2 + 4xy = 200

4xy = 200 − x 2
200 − x 2
y =
4x

Substituting into the volume formula,
2
V = x y
2
200 − x
2
V (x) = x
4x
2
200 − x
V (x) = x
4
200x − x 3
V (x) =
4

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