A window with a 20-foot perimeter (frame) is to be comprised of a semi-circular stained glass pane above a rectangular clear pane as shown in the accompanying figure.

Question

A window with a 20-foot perimeter (frame) is to be comprised of a semi-circular stained glass pane above a rectangular clear pane as shown in the accompanying figure. Clear glass costs $3 per square foot and stained glass costs $10 per square foot. Express the cost of the window as a function of the radius of the stained glass pane.

the diameter of the glass pane is represented as x.

The side of the rectangular clear pane is represented by y.

While the base of the window is represented by 2x.

Answer 1

Given: Window with semi-circular stained-glass on top of rectangular clear-glass.

Clear glass costs $3 per ft^2 and stained glass costs $10 per ft^2.

Let x = radius of stained glass pane. *** THIS IS A CORRECTION ***

Let y = side of clear rectangular window.

Base of window is represented by 2x. (So, radius must be x)

Find: Express cost of window as a function of the radius of stained glass pane.

Solution:

C = Cost

C = (Area of semi-circular pained glass)*10 + (Area of rectangular clear glass)*3

C = (1/2)(pi*x^2)*10 + (2x*y)*3

C = 5*pi*x^2 + 6*x*y