Question

A circle has a radius of 10 inches. The circumference of the circle is c inches. Which expression best represents the value of π? A10c C20 1 1- 2 B10 D20c step by step on how u got the answer

Answer 1

To find an expression for \(\pi\) in terms of the given radius and the circumference of a circle, we start with the formulas related to a circle.

1. **Understand the Formula for Circumference**:
The circumference \(C\) of a circle is given by the formula:
\[
C = 2\pi r
\]
where \(r\) is the radius.

2. **Given Radius**:
In this case, we are given a radius \(r = 10\) inches.

3. **Substituting the Radius into the Formula**:
If we substitute the radius into the circumference formula, we get:
\[
C = 2\pi(10) = 20\pi
\]
This means that the circumference \(C\) can be expressed as \(20\pi\).

4. **Isolating \(\pi\)**:
Now, we want to express \(\pi\) in terms of the circumference \(C\). We can do this by solving for \(\pi\):
\[
\pi = \frac{C}{20}
\]

5. **Identifying the Expression**:
We want to choose the correct expression for \(\pi\) given the options presented:
- A: \(10c\)
- B: \(10\)
- C: \(20\)
- D: \(\frac{20}{C}\)

6. **Choosing the Correct Option**:
The expression we derived gives us:
\[
\pi = \frac{C}{20}
\]
To put it in the forms given:
We can rearrange \(\frac{C}{20}\) as:
\[
\frac{1}{20}C \implies D = \frac{20}{C}
\]

Given that we're looking for the expression that best represents \(\pi\), none of the given options directly match \(\pi = \frac{C}{20}\) without additional manipulation.

Therefore, option **D (twenty divided by c)** corresponds with our formula because, if \(C = 20\pi\), then \(\pi = \frac{C}{20}\).

Thus, the answer is:

### D: \(\frac{C}{20}\) which represents \(\pi\) given the context of circumference.