A square is inscribed in a circle. If the area of the square is 9 in2, what is the ratio of the circumference of the circle to the area of the circle?
To find the ratio of the circumference of the circle to the area of the circle, we first need to find the circumference and the area of the circle.
Let's start by finding the circumference of the circle. The circumference of a circle can be calculated using the formula C = 2πr, where C represents the circumference and r represents the radius of the circle.
Since the square is inscribed in the circle, the diagonal of the square will be equal to the diameter of the circle. Let's find the diagonal of the square.
Given that the area of the square is 9 in^2, we can calculate its side length. The area of a square is equal to the side length squared, so we can find the side length by taking the square root of the area.
√9 in^2 = 3 in
Since the diagonal of a square is √2 times the side length, we can find the diagonal by multiplying the side length by √2.
Diagonal of the square = 3 in * √2
Now, we know that the diagonal of the square is equal to the diameter of the circle. So the diameter of the circle is 3 in * √2.
Since the diameter is twice the radius, we can find the radius by dividing the diameter by 2.
Radius of the circle = (3 in * √2) / 2
Now that we have the radius, we can find the circumference of the circle using the formula C = 2πr.
Circumference of the circle = 2π * (3 in * √2 / 2)
Simplifying further:
Circumference of the circle = 3π√2 in
Moving on to find the area of the circle. The area of a circle is calculated using the formula A = πr^2, where A represents the area and r represents the radius of the circle.
Area of the circle = π * [(3 in * √2 / 2)^2]
Simplifying further:
Area of the circle = 2π(3 in)^2 / 4
Area of the circle = 9π in^2
Finally, to find the ratio of the circumference of the circle to the area of the circle, we divide the circumference by the area:
Ratio = (3π√2 in) / (9π in^2)
Simplifying further:
Ratio = √2 / 3
Therefore, the ratio of the circumference of the circle to the area of the circle is √2 / 3.
each side of the square is 3in
so radius is 1.5in
AreaCircle=PI*2.25
circumference=PI*3
what is 3/2.25 ?