Question

the diameter of a circle is $12\frac{1}{3}$ inches. what is the radius, $r$, of the circle? enter your answer as a mixed number in simplest form by filling in the boxes. $r = \square \frac{\square}{\square}$ in.

Explanation:

Step1: Recall radius-diameter relation

The radius $r$ is $\frac{1}{2}$ of the diameter $d$, so $r = \frac{d}{2}$.

Step2: Substitute diameter value

The diameter $d = 12\frac{1}{3} = \frac{37}{3}$ inches. Substitute into the formula:
$r = \frac{1}{2} \times \frac{37}{3}$

Step3: Calculate and convert to mixed number

Multiply the fractions: $\frac{37}{6} = 6\frac{1}{6}$

Answer:

$r = 6\frac{1}{6}$ in.