Question

A circle is placed in a square with a side length of , as shown below. Find the area of the shaded region.Use the value for , and do not round your answer. Be sure to include the correct unit in your answer.

Answer 1

SOLUTION

The diameter of the circle is the same as the lenght of a side of the square, hence the diameter is 4 ft

The radius of the circle becomes

$radius=\frac{diameter}{2}=\frac{4}{2}=2\text{ ft}$

so the radius of the circle is 2 ft.

The area of the shade region is calculated as

$area\text{ of shaded region = area of square - area of circle}$

area of square becomes

$\begin{gathered} area\text{ of square = length}\times length \\ =4\times4 \\ =16\text{ ft}^2 \end{gathered}$

area of the circle becomes

$\begin{gathered} area\text{ of circle = }\pi r^2 \\ =3.14\times2^2 \\ =3.14\times4 \\ =12.56\text{ ft}^2 \end{gathered}$

So, the shaded area becomes

$\begin{gathered} area\text{ of shaded region = area of square - area of circle} \\ =16-12.56 \\ =3.44\text{ ft}^2 \end{gathered}$$3.44\text{ ft}^2$