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
l
.
If the cost of the framing material is $
11
11
per linear foot and the cost of the pane glass is $
27
27
per square foot, what is the total cost of a window with a base length of
4
4
feet?
Write a function named
C
C
that relates the total cost of the window to the length of the base of the window,
l
l
.
Proof-read and fix your post
if the base has diameter d, then
the area is 1/8 pi d^2
the perimeter is d + 1/2 pi d
Now just multiply each of those values by their cost, and add it up.
To calculate the total cost of a window with a base length of l feet, we need to consider the cost of the glass pane and the cost of the framing material.
The cost of the framing material is given as $11 per linear foot. Therefore, the cost of the framing material for a window with a base length of l feet would be 11 * l dollars.
The cost of the glass pane is given as $27 per square foot. The area of a semi-circular window can be calculated using the formula (π * l^2) / 8, where l is the base length. So, the cost of the glass pane for a window with a base length of l feet would be 27 * [(π * l^2) / 8] dollars.
To calculate the total cost, we need to add the cost of the framing material and the cost of the glass pane.
Therefore, the function C(l) that relates the total cost of the window to the length of the base of the window, l, would be:
C(l) = (11 * l) + (27 * [(π * l^2) / 8])
To find the total cost of a window with a base length of 4 feet, we simply substitute l = 4 into the function C(l) and perform the calculations:
C(4) = (11 * 4) + (27 * [(π * 4^2) / 8])