Page 99 - How To Solve Word Problems In Calculus

Solution
Step1

πr

r

x x

2r

Step2
The area of the window is the sum of the areas of its
rectangular bottom and its semicircular top. Since the area of
2
a whole circle of radius r is πr , a semicircle has an area of
1 2
πr .
2

1 2
A = 2rx + πr
2

Step3
The window has 4 sides, 3 straight sides and a semicircular
top. Since the circumference of a whole circle of radius r is 2πr,
the semicircular arc has length πr. Since the perimeter is 20 ft,

2x + 2r + πr = 20
20 − 2r − πr
x =
2

We substitute into the equation obtained in step 2 and obtain
the area as a function of r.

86