From a piece of pin in the shape of a square 6 inches on a side, the largest possible circle is cut out. Of the following, the ratio of the area of the circle to the area of the original square is closest in value to
A. 4/5
B. 3/5
C. 2/3
D. 1/2
Area of square = 6 * 6 = 36 square inches
Are of circle = 3.14 * 9 = 28.26 square inches
To find the ratio of the area of the circle to the area of the square, we need to calculate the area of both shapes.
Area of the square:
The area of a square is given by the formula A = s^2, where s is the length of one side of the square. In this case, the length of the side is 6 inches, so the area of the square is 6^2 = 36 square inches.
Area of the circle:
The area of the circle is given by the formula A = πr^2, where π is a constant (approximately 3.14) and r is the radius of the circle.
To find the radius of the circle, we need to use the fact that the diameter of the circle is equal to the length of each side of the square. Since the side length of the square is 6 inches, the diameter of the circle is also 6 inches.
The radius of the circle is half the diameter, so the radius is 6/2 = 3 inches.
Therefore, the area of the circle is A = π(3^2) = 9π square inches.
Now, let's compare the ratio of the area of the circle to the area of the square:
Ratio = (Area of the circle) / (Area of the square)
= (9π) / 36
≈ 0.785 ≈ 0.79
To determine the closest value provided in the options, let's convert each option to decimal form:
A. 4/5 ≈ 0.8
B. 3/5 ≈ 0.6
C. 2/3 ≈ 0.67
D. 1/2 = 0.5
Based on the closest values, we can see that the ratio of the area of the circle to the area of the square is closest in value to option A. Therefore, the answer is A. 4/5.