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 = xr² where r = 3.14)
a. 15 ft
b. 30 ft²
c. 60 ft
d. 90 ft²

Answer 1

The approximate remaining area of the board after cutting out the largest possible circle from a square with a side length of 12 feet is 30 square feet.

Step-by-step explanation:

To determine the approximate area in square feet of the board remaining after the largest possible circle is cut out of a square with side length is 12 feet, we first find the area of the original square and then subtract the area of the circle.

The area of the square is calculated as side length × side length, which equals 12 feet × 12 feet = 144 square feet.

The diameter of the largest circle that can fit within the square is equal to the side length of the square, so the radius is half of that: 12 feet / 2 = 6 feet.

Using the formula for the area of a circle A = πr² where π (pi) is approximately 3.14 and r is the radius, we get:

A = 3.14 × (6 feet)² = 3.14 × 36 = 113.04 square feet.

To find the remaining area of the board, we subtract the area of the circle from the area of the square:

144 square feet - 113.04 square feet ≈ 30.96 square feet.

Since the answer is approximate, we can round this to 30 ft², which is the closest answer among the options provided.