Question

$\overline{ab}$ is a radius of the circle. the circumference of the circle is 189.73. find the length of $\overline{ab}$, rounding to the nearest tenth.

Explanation:

Step1: Recall the formula for the circumference of a circle

The formula for the circumference of a circle is \(C = 2\pi r\), where \(C\) is the circumference and \(r\) is the radius.

Step2: Solve for the radius \(r\)

Given \(C=189.73\) and taking \(\pi\approx3.14\). Substitute into the formula:
\(189.73 = 2\times3.14\times r\)
First, calculate \(2\times3.14 = 6.28\). Then the equation becomes \(189.73=6.28r\).
To find \(r\), we use \(r=\frac{189.73}{6.28}\).
\(r=\frac{189.73}{6.28}\approx30.2\) (rounded to the nearest tenth)

Answer:

\(30.2\)