The largest possible circle is cut out of a square whose side length is 12 feet. What will be the approximate area, in square feet, of the remaining board? ( A= pie r square where pie=3.14 )
Question
The largest possible circle is cut out of a square whose side length is 12 feet. What will be the approximate area, in square feet, of the remaining board? ( A= pie r square where pie=3.14 )
Solution
Step 1: Find the diameter of the circle. Since the circle is cut out of a square, the diameter of the circle is equal to the side length of the square, which is 12 feet.
Step 2: Find the radius of the circle. The radius is half of the diameter, so the radius of the circle is 12/2 = 6 feet.
Step 3: Find the area of the circle using the formula A = πr². Substituting π = 3.14 and r = 6, we get A = 3.14 * (6)² = 3.14 * 36 = 113.04 square feet.
Step 4: Find the area of the square. The area of a square is side length squared, so the area of the square is 12² = 144 square feet.
Step 5: Subtract the area of the circle from the area of the square to find the area of the remaining board. So, the area of the remaining board is 144 - 113.04 = 30.96 square feet.
So, the approximate area of the remaining board is 30.96 square feet.
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