Question

The radius of a circle is 10. Using π, which equation expresses the ratio of the circumference of the circle to the circle's diameter?
Responses
A




= πC 10 = π
B




= πC 20 = π
C C =
π




C = 10 π r
D C =
π

Answer 1

To express the ratio of the circumference of a circle to the circle's diameter, we can use the formulas related to the circumference (C) and diameter (d) of a circle:

1. The formula for the circumference of a circle is:
\[ C = 2\pi r \]
where \( r \) is the radius. In this case, the radius is 10, so:
\[ C = 2\pi(10) = 20\pi \]

2. The formula for the diameter of a circle is:
\[ d = 2r \]
So for a radius of 10, the diameter is:
\[ d = 2(10) = 20 \]

Now, the ratio of the circumference to the diameter is given by:
\[
\text{Ratio} = \frac{C}{d} = \frac{20\pi}{20} = \pi
\]

From the provided options, the correct equation expressing that ratio is:

**B: \( \frac{C}{20} = \pi \)**

Thus, the ratio of the circumference of the circle to the circle's diameter is indeed \( \pi \).