Question

In order to make a circular sign, you decide to use a square piece of plywood and trim off as little of the area as possible. Write a simplified formula for A, the least possible area of wood that you will not use, given that one edge of the square has length W?

Answer 1

The area of the square is W^2

The area of the circle will be PI * radius^2
where the radius = (W/2)
So, the circle area = PI * (W/2)^2 = PI * (W^2 /4)

If square has a 12 inch side its area is 144 square inches.
The circle would be PI * (144 / 4) = PI * 36 =
113.0973355292 square inches

So, A = (W^2) - (PI * (W^2 / 4)