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23 November, 07:52

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.

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  1. 23 November, 10:41
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    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
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