Page 22 - How To Solve Word Problems In Calculus

4x 2πr
12
x

r
x

Step2

2
A = x + πr 2

Step3
Since the combined perimeter of the two figures must be
12 inches, we have

4x + 2πr = 12

It follows that

2πr = 12 − 4x
12 − 4x 6 − 2x
r = =
2π π

Replacing r in terms of x in step 2 gives the area as a function
of x.

6 − 2x 2
2
A(x) = x + π
π
(6 − 2x) 2
2
= x +
π
If all the wire is used to form the circle, x = 0. If all the wire is
used for the square, 4x = 12 and x = 3. Our function is

(6 − 2x) 2
2
A(x) = x + 0 ≤ x ≤ 3
π
9