Homework SourseA Norman window has the shape of a semicircle atop a rectang
A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of the rectangle. What is the area of the largest possible Norman window with a perimeter of 26 feet?
Solution
A = pi d^2 /8 + d * h 30 = pi d + d + 2 h h = [30 - (1+pi)d] / 2 A = pi d^2 /8 + d * [30 - (1+pi)d] / 2 = (pi/8 - pi/2)d^2 + 15 d A = (-3pi/8) d^2 + 15 d dA/dd = (-3pi/4) d +15 = 0 ___ take the derivative and set to 0 d = 15 * (4/3pi) = 20/pi = A = (-3/8) 400/pi + 300/pi A = 150/pi = 47.75 sq ft
