Chapter 6, Problem 19SGA

To determine

To find:The length of the intercepted arc in a circle of radius $15\text{cm}$ with $150°$ central angle.

Answer to Problem 19SGA

The length of the intercepted arc in a circle of radius $15\text{cm}$ with $150°$ central angle to the nearest tenthis $39.3\text{cm}$ .

Explanation of Solution

Given information:

The measure of the central angle is $150°$ and the radius of circle is equal to $15\text{cm}$ .

Formula used: The formula for the length of intercepted arc of a circle is the product of radius with central angle.

  $s=r\theta$

Calculation:

Convert the central angle into radian.

  $150°\times \frac{\pi }{180°}=\frac{5\pi }{6}$

So, the measurement of central angle in radian is equal to $\frac{5\pi }{6}$ .

Substitute $15\text{cm}$ for $r$ and $\frac{5\pi }{6}$ for $\theta$ in the formula for the length of intercepted arc.

  $\begin{array}{c}s=r\theta \\ =\left(15\text{cm}\right)\left(\frac{5\pi }{6}\right)\\ =\frac{75}{6}\times 3.14\\ =39.25\text{cm}\end{array}$

The answer rounded to nearest tenth is equal to $39.3\text{cm}$ .

Therefore, the length of the intercepted arc in a circle of radius $15\text{cm}$ with $150°$ central angle is $39.3\text{cm}$ .