Question

e. A semicircular window with a radius of

36 inches allows light through an area of how

many square feet? You may use a calculator

if one is available. Round your answer to the

nearest square foot.

Answer 1

Answer:

14 sq. ft $(14 ft^{2})$

Step-by-step explanation:

First, we know that the area of a circle is $\\ A_{circle} =\pi * r^{2}$, where r is the radius of the circle, and $\pi$ is the ratio of the length of a circle's circumference to its diameter, that is, $\pi$=3.1415926535 ... . But we have here a semicircle.

So, the area of a semicircle is $\\ A_{semicircle} = \frac{1}{2} (\pi * r^{2})$.

We also know that 1 feet = 12 inches, so 36 inches are:

$\\ \frac{1ft}{12inches} * 36 inches = 3 ft$

Then, the area of the semicircular window is:

$\\ A_{semicircular-window} = \frac{1}{2} (\pi * 3^{2})$ ≈ 14.1372.

Well, rounding the answer to the nearest square foot, we have that the semicircular window allows light through an area of 14 sq. ft $(14 ft^{2})$.