A circle has its center at the center of a square with 12-inch sides. Using 3.14 for pi, find the area of the square not covered by the circle, then write a ratio of the circle’s circumference to the perimeter of the square.
area of square = 144 inches^2
area of circle = 36π inches^2
area not in circle = 144-36π
ratio of circumf : perim = 2π(6) : 48
= 12π : 48
= π : 4
To find the area of the square not covered by the circle, we need to subtract the area of the circle from the total area of the square.
First, let's find the area of the circle. The diameter of the circle is equal to the side length of the square, which is 12 inches. The radius of the circle is half the diameter, so it is 12/2 = 6 inches.
The formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius. Using π = 3.14 and r = 6 inches, we can calculate the area of the circle as A = 3.14 * 6^2 = 3.14 * 36 = 113.04 square inches.
Now, let's find the area of the square. The formula to calculate the area of a square is A = side^2, where A is the area and side is the side length. Using the side length of 12 inches, the area of the square is A = 12^2 = 144 square inches.
To find the area of the square not covered by the circle, we subtract the area of the circle from the area of the square: 144 - 113.04 = 30.96 square inches.
So, the area of the square not covered by the circle is 30.96 square inches.
Now, let's calculate the ratio of the circle's circumference to the perimeter of the square.
The formula to calculate the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. Using π = 3.14 and r = 6 inches, we can calculate the circumference of the circle as C = 2 * 3.14 * 6 = 2 * 3.14 * 6 = 37.68 inches.
The formula to calculate the perimeter of a square is P = 4s, where P is the perimeter and s is the side length. Using the side length of 12 inches, the perimeter of the square is P = 4 * 12 = 48 inches.
So, the ratio of the circle's circumference to the perimeter of the square is 37.68 inches : 48 inches, which can also be simplified as 31/40 or 0.775.