Page 26 - How To Solve Word Problems In Calculus

EXAMPLE 8
A closed box has a base twice as long as it is wide. If its volume
3
is 100 in , express its surface area as a function of the width x
of its base.

Solution
Step1
Since the base of the box is a rectangle whose length
is twice its width, we can represent its dimensions by x and
2x. The height, however, must be represented by a different
variable.

y
x

2x

Step2
The surface area of the box S is the sum of the areas of
2
its six sides. The top and bottom areas are each 2x , the front
and back areas are each 2xy, and the left and right sides each
have an area of xy.
2
2
S = 2x + 2x + 2xy + 2xy + xy + xy
2
S = 4x + 6xy

Step3
3
2
The volume of the box (l × w × h), 2x y, is 100 in .
2
2x y = 100
50
y =
x 2

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