Question

What will be the aproximate area in squre feet of the remaining board?

Answer 1

Given:

The largest possible circle is cut out of a square whose side lenght is 12 feet.

The area of square is given by,

`\begin{gathered} A=(side)^2 \\ A=12^2=144 \end{gathered}`

The radius of circle will be,

`r=(12)/(2)=6\text{ f}eet`

And the area of circle is ,

`\begin{gathered} A=\pi(r)^2 \\ A=\pi(6)^2 \\ A=36\pi \end{gathered}`

The area left when circle is cut out of a square is ,

`\begin{gathered} \text{Area left = 144- 36}\pi \\ =30.9\text{ }\approx31\text{ square f}eet \end{gathered}`

Hence, the required area is 31 square feet.