Question

What is the approximate area of the remaining portion of the circle in square feet?

Answer 1

Given a circle of approximately 14 feet in diameter, d.

A square of side length 10 feet is cut out of the circle.

To find the area of the shaded portion, i.e. the remaining part, we subtract the area of the square from the area of the circle since the square is being cut out and not shaded in the given figure.

The formula to find the shaded area, A, is

`\begin{gathered} A=Area\text{ of circle}-Area\text{ of square} \\ A=\pi r^2-l^2 \\ Where\text{ r is the radius of the circle} \\ l\text{ is the side length of the square} \end{gathered}`

Where,

The radius, r, is

`\begin{gathered} r=(d)/(2)=(14)/(2)=7\text{ ft } \\ r=7\text{ ft} \end{gathered}`

And the side length, l, of the square is 10ft

Substitute for r and l into the formula above

`\begin{gathered} A=\pi r^2-l^2 \\ Where\text{ }\pi\approx3.14 \\ A=(3.14*7^2)-(10^2) \\ A=153.86-100=53.86\text{ ft}^2 \\ A=53.86\text{ ft}^2 \end{gathered}`

Since, the area, A, of the shaded region is 53.86 ft², the approximate area will be

`A=50\text{ ft}^2\text{ \lparen approx\rparen}`

Hence, the answer is 50 ft²