One circle has a circumference half as large as that of a second circle. Which ratio compares the diameter of the first circle to the diameter of the second circle
The circumference of a circle is directly proportional to its diameter, so if one circle has a circumference that is half as large as another circle, it must have a diameter that is also half as large. Therefore, the ratio of the diameter of the first circle to the diameter of the second circle is:
1:2 (or 1/2)
The ratio comparing the diameter of the first circle to the diameter of the second circle can be found using the relationship between circumference and diameter of a circle.
The formula states that the circumference of a circle is equal to π times the diameter.
Let's assume the circumference of the second circle is C2 and the circumference of the first circle is C1. Given that C1 is half the size of C2, we have C1 = (1/2)C2.
Using the formula for circumference, we have C = πd, where C is the circumference and d is the diameter.
So, for the first circle, we have C1 = πd1, and for the second circle, we have C2 = πd2.
Substituting the values for C1 and C2, we get (1/2)C2 = πd1 and rearranging the equation gives d1 = (1/2π)C2.
Therefore, the ratio comparing the diameter of the first circle (d1) to the diameter of the second circle (d2) is:
d1/d2 = ((1/2π)C2) / (C2/π)
Simplifying the expression, we find that d1/d2 = 1/2.
Thus, the ratio comparing the diameter of the first circle to the diameter of the second circle is 1:2.