please help

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 length of frame needed for a window with a base length of 4 feet.

b) Write a function named h that expresses the total length of the frame in terms of the length of the base of the window

c) If the cost of the framing material is $12 per linear foot, what is the cost of a window frame with a base length of 4 feet?

Answer 1

Hi Zeze,

 

a) If you make a diagram of the window, place the four feet line at the bottom and a semicircle extending from one end to the other.  You can see that half of the base (2 feet) is the radius of the semicircle.  So the length of the semicircle (half the circumference of a full circle) is pi x r = 2pi and the total frame is 4 + 2pi.  You can substitute a number for pi if you want to (3.14....)

 

b) Therefore the function should be . . . H(L) = L + (L x pi/2)

 

c) The cost is 12 x (4 + 6.28) = 12 x 10.28 = $123.36.  If you have to buy the framing material by the foot, then you'll have to order 11 feet (not 10.8 feet) and the cost would be $132.00

 

Dan