Question

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.

Answer 1

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