Question

The circumference of a circle is 37.68 centimeters. What is the circle's radius?
Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.
centimeters

Answer 1

To find the radius of a circle given its circumference, we can use the formula for the circumference of a circle:

\[
C = 2\pi r
\]

where:
- \( C \) is the circumference,
- \( r \) is the radius, and
- \( \pi \) is approximately 3.14.

Given that the circumference \( C = 37.68 \) centimeters, we can rearrange the formula to solve for the radius \( r \):

\[
r = \frac{C}{2\pi}
\]

Substituting the given values into the formula:

\[
r = \frac{37.68}{2 \times 3.14}
\]

Calculating the denominator:

\[
2 \times 3.14 = 6.28
\]

Now, substituting this value back into the formula for \( r \):

\[
r = \frac{37.68}{6.28} \approx 6.0
\]

To find the radius more precisely:

\[
r \approx \frac{37.68}{6.28} \approx 5.99
\]

Rounding to the nearest hundredth gives us:

\[
r \approx 5.99 \, \text{centimeters}
\]

So, the radius of the circle is approximately \( 5.99 \) centimeters.