Question

find the radius of a circle with a circumference of 28.26 cm.

Explanation:

Step1: Recall the formula for circumference of a circle

The formula for the circumference \( C \) of a circle is \( C = 2\pi r \) (where \( r \) is the radius) or \( C=\pi d\) (where \( d \) is the diameter, and \( d = 2r \)). We can also write the formula to solve for \( r \) as \( r=\frac{C}{2\pi}\). We will use \( \pi\approx3.14 \) for calculation.

Step2: Substitute the given circumference into the formula

Given that \( C = 28.26\space\text{cm} \) and \( \pi\approx3.14 \), substitute these values into the formula \( r=\frac{C}{2\pi} \).
\[
r=\frac{28.26}{2\times3.14}
\]
First, calculate the denominator: \( 2\times3.14 = 6.28 \). Then, divide \( 28.26 \) by \( 6.28 \):
\[
r=\frac{28.26}{6.28}=4.5
\]

Answer:

The radius of the circle is \( 4.5\space\text{cm} \).