The largest possible circle is cut out of a square whose side length is 8 feet. What will be the approximate area, in square feet, of the remaining board? ( where

13.76ft²

Step-by-step explanation:

Side of square: d=8ft

Area of board: Sb=d×d=64ft²

Area of circle: Sc=pi×r²=pi×(d/2)²=pi×d²/4=pi×64/4= 16×pi=50.24ft²

Remainin area: Sb-Sc=64-50.24=13.76ft²

Area of remaining board is 13.728 feet²

Step-by-step explanation:

Given; Square side length = 8 feet

Therefore, the diameter of the cut out circle = 8 feet, then Radius = 4 feet

The approximate area, in square feet, of the remaining board will be the are of the square minus the ares of the cut out circle.

Area of the square =  S²

                                = (8 feet)²

                                = 64 feet²

Area of the cut circle = π(4 feet)²

                                   = 3.142 x 16 feet²

                                   = 50.272 feet²

Area of remaining board = Area of the square - Area of the cut circle

Area of remaining board = 64 feet² - 50.272 feet²

Area of remaining board = 13.728 feet²