The cost of manufacturing a semicircular window is the cost

The cost of manufacturing a semi-circular window is the cost of the glass pane together with the cost of the framing material. When ordering this window, customer specifies the length of the base of the window, shown as l. If the cost of the framing material is $10 per linear foot and the cost of the pane glass is $23 per square foot, what is the total cost of a window with a base length of 4 feet? Write a function named C that relates the total cost of the window to the length of the base of the window, l.

Solution

Area of glass pane = area of semicircle = pi(l^2)/8

l = dia of semi circle

Given l= 4feet

Area of glass plane = pi(l^2)/8= pi(4)^2/8 =2pi feet^2= 6.28 feet^2

Lenght of framing material = circumefernec of semicicle = l + pi*(l/2)

= 4 + pi(4)/2 =10.28 feet

a) So, cost of window = 10.28 x10 + 6.28x 23 = $247.24

b) C(l) = 10(l + pi*(l/2)) + 23(pi(l^2)/8