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

14 sq. ft
`(14 ft^(2))`

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) = (1)/(2) (\pi * r^(2))`.

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

`\\ (1ft)/(12inches) * 36 inches = 3 ft`

Then, the area of the semicircular window is:

`\\ A_(semicircular-window) = (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))`.