Question

a circular stained - glass window costs $65 per square foot to build. if the diameter of the window is 6 ft, find the cost to build the window. round to the nearest dollar. (use 3.14 for $pi$)

Explanation:

Step1: Find the radius of the circle

The radius $r$ is half of the diameter. Given diameter $d = 6$ ft, so $r=\frac{d}{2}=\frac{6}{2}=3$ ft.

Step2: Calculate the area of the circle

The area formula of a circle is $A=\pi r^{2}$. Using $\pi = 3.14$ and $r = 3$ ft, we have $A=3.14\times3^{2}=3.14\times9 = 28.26$ square - feet.

Step3: Calculate the cost to build the window

The cost per square - foot is $65$ dollars. So the total cost $C=65\times A$. Substituting $A = 28.26$ square - feet, we get $C=65\times28.26=1836.9\approx1837$ dollars.

Answer:

$1837$