A stained glass window is going to be installed in a semi-circular opening, which is above a 30 inch wide door. If the stained glass window costs $1.40 per square inch, how much will the window cost? Use 3.14 for π as necessary.

The answer is $494.55

Let's first imagine a circle and calculate its area and then reduce it in half for the area of a semi-circle. Since this opening is above a 30-inch wide door, the circle will have a diameter of 30 inches.

The area of the circle (A) is:

A = π · r²

where:

π = 3.14

r - radius: r = diameter : 2 = 30 : 2 = 15 inches

So, the area of the circle is:

A = π · r² = 3.14 · 15² = 706.5 inches²

The area of the semicircle is half of the area of the circle:

A1 = A : 2 = 706.5 : 2 = 353.25 inches²

Since the stained glass window costs $1.40 per square inch, for 353.25 square inches it will cost $494.55:

353.25 square inches * 1.40 $/square inch = $494.55