The cost of manufacturing a semi-circular window is the cost of the glass pane t

Question

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, a customer specifies the length of the base of the window, shown as l. a. If the cost of the framing material is $12 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 related the total cost of the window to the length of the nearest penny. If the glass pane costs $23 per square foot, what's the cost of a glass pane with the window base is 2 feet? Use you answer to part a), and round to the nearest penny. Determine the largest possible window you can buy if the most you can spend on the glass pane is $350. What should you specify for the base window length?

Explanation / Answer

a) , b) base length = dia of semi circle = l

Ares of semicirle , K(l) = (1/2)(pi)(l/2)^2 = pi*l^2/8

if l = 2 ft

K(5) = pi*2^2/8 = pi/2 = 1.57 sqft

c) cost of glass = $ 23 sqfoot

So, cost of window = 23*1.57= $ 36.11

d) largest window area you can buy = total money/cost of 1 square foot of glass = 350/23 = 15.217 sqfoot

pi*l^2/8 = 15.217

l = 6.22 = 6 foot ( base length)

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