Q:

The largest possible circle is to be cut from a 12-foot square board. Calculate the approximate area, in square feet, of the remaining board (unshaded region)? (A = πr2). (pic is in question comments)

Accepted Solution

A:
------------------------------------------------------------------------------
Find Area of the circle:
------------------------------------------------------------------------------
Area of a circle = πr²
Area of the largest possible circle = π x(12 ÷ 2)²
Area of the largest possible circle = 113.10 ft²

------------------------------------------------------------------------------
Find Area of the square board:
------------------------------------------------------------------------------
Area of a square board = Length x Length
Area of the square board = 12 x 12 
Area of the square board = 144 ft²

------------------------------------------------------------------------------
Find area of the remaining board:
------------------------------------------------------------------------------
Area of the remaining board = 144 - 113.10 
Area of the remaining board = 30.90 ft²

------------------------------------------------------------------------------
Answer: The area of the remaining board is 30.90 ft².
------------------------------------------------------------------------------