how many 30" circles can be cut from 4'x8' board
To find out how many 30" circles can be cut from a 4'x8' board, we need to consider both the dimensions of the board and the size of the circles.
First, let's convert the dimensions of the board and the circle from inches to feet for consistent units:
4 feet = 48 inches
8 feet = 96 inches
30 inches = 2.5 feet
Next, we need to find the area of the board and the area of the circle.
The area of a rectangle (board) is given by the formula: Area = Length x Width
Area of the board = 48 inches x 96 inches = 4,608 square inches
Converting the area to square feet: 4,608 square inches ÷ 144 square inches/square foot = 32 square feet
The area of a circle is given by the formula: Area = π x (radius)^2
Since we know the diameter of the circle is 30 inches, the radius is half of the diameter, which is 15 inches.
Converting the radius to feet: 15 inches ÷ 12 inches/foot = 1.25 feet
Area of the circle = 3.14 x (1.25 feet)^2 = 4.91 square feet (rounded to two decimal places)
Now, we can divide the area of the board by the area of the circle to find out how many circles can be cut.
Number of circles = Area of the board ÷ Area of the circle = 32 square feet ÷ 4.91 square feet (rounded to two decimal places)
Using a calculator, the number of circles is approximately 6.52.
Therefore, you can cut approximately 6 to 7 (rounded down) 30-inch circles from a 4'x8' board.