Question

find the length of arc abc. use 3.14 for the value of π. 63 cm 240° ? cm round your answer to the nearest hundredth.

Explanation:

Step1: Recall the arc length formula

The formula for the length of an arc is $L=\frac{\theta}{360^{\circ}}\times2\pi r$, where $\theta$ is the central angle in degrees and $r$ is the radius of the circle.

Step2: Identify the values of $\theta$ and $r$

From the diagram, the radius $r = 63$ cm and the central angle for arc $ABC$ is $\theta=240^{\circ}$. We are given that $\pi = 3.14$.

Step3: Substitute the values into the formula

First, calculate $2\pi r$: $2\times3.14\times63 = 395.64$ cm.
Then, find the fraction of the circle corresponding to the arc: $\frac{240^{\circ}}{360^{\circ}}=\frac{2}{3}$.
Now, multiply this fraction by the circumference ($2\pi r$) to get the arc length: $L=\frac{2}{3}\times395.64$.

Step4: Perform the multiplication

$\frac{2}{3}\times395.64 = 263.76$ cm.

Answer:

263.76