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. Determine the total area of glass pane needed for a window with a base length of 5 feet. Round your answer to the nearest hundredth of a square foot.

b. Write a function named k that relates the area of the glass pane to the length of the base of the window. k(l) = help (formulas)

c. If the glass pane costs $23 per square foot, what's the cost of a glass pane with the window base is 5 feet? Use your answer to part a), and round to the nearest penny.

d. 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? Round your answer to the nearest tenth of a foot.

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 = 5 ft

K(5) = pi*5^2/8 = 9.817 ft^2

c) cost of glass = $ 23 sqfoot

So, cost of window = 23*9.817 = $ 225.80

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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