To find the circumference, Elspeth can follow these detailed steps:
1. Understand the given information:
- Elspeth knows that the product of [tex]\(\pi\)[/tex] and the radius [tex]\(r\)[/tex] is approximately [tex]\(9.42 \text{ cm}\)[/tex]. This can be written as:
[tex]\[
\pi \cdot r \approx 9.42
\][/tex]
2. Solve for the radius [tex]\(r\)[/tex]:
- To find [tex]\(r\)[/tex], Elspeth can divide the given value [tex]\(9.42 \text{ cm}\)[/tex] by [tex]\(\pi\)[/tex]:
[tex]\[
r = \frac{9.42}{\pi}
\][/tex]
3. Substitute the approximate value of [tex]\(\pi \approx 3.14159\)[/tex] into the equation:
[tex]\[
r = \frac{9.42}{3.14159} \approx 2.998
\][/tex]
Here, [tex]\(r\)[/tex] is approximately [tex]\(2.998 \text{ cm}\)[/tex].
4. Calculate the circumference:
- Recall the formula for the circumference of a circle, which is [tex]\(C = 2 \pi r\)[/tex].
- Substitute the approximate values of [tex]\(\pi\)[/tex] and the calculated radius into the formula:
[tex]\[
C = 2 \cdot 3.14159 \cdot 2.998 \approx 18.84 \text{ cm}
\][/tex]
5. Summarize the process:
- First, Elspeth divided [tex]\(9.42 \text{ cm}\)[/tex] by [tex]\(\pi\)[/tex] to find the radius.
- Then, she used the formula [tex]\(C = 2 \pi r\)[/tex] to find the circumference.
Therefore, Elspeth should:
- Divide [tex]\(9.42 \text{ cm}\)[/tex] by [tex]\(\pi\)[/tex] to find the radius, and then
- Multiply this radius by [tex]\(2 \pi\)[/tex] to find the circumference.
Given the above steps, the calculated radius is approximately [tex]\(2.998 \text{ cm}\)[/tex], and the final circumference is approximately [tex]\(18.84 \text{ cm}\)[/tex].
