Page 108 - How To Solve Word Problems In Calculus

Step2
The volume of a box is length × width × height. Accord-
2
ing to the diagram, V = x y.
Step3
The surface area of the box is the sum of the areas of its
2
six sides. The top and bottom each have an area of x and each
of the four sides of the box has an area of xy.
2
2x + 4xy = 150
2
x + 2xy = 75
75 − x 2
y =
2x

75 − x 2
V(x) = x 2
2x
x 2
= (75 − x )
2
1 3
= (75x − x )
2
Step4
1
2
V (x) = (75 − 3x )
2
1
2
0 = (75 − 3x )
2
0 = 75 − 3x 2
2
3x = 75
2
x = 25
x = 5

75 − x 2 75 − 25 50
y= = = = 5; the corresponding volume =
2x 10 10
3
2
x y = 125 in .
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