DIf the radius of the circle is 6cm, what is the length of arc BC? Round to the nearestthousandth (3 decimal places) and use the pi button on the calculator.

Question

asked Nov 9, 2023 63.1k views

1 Answer

Michael Logutov · Answer 1 · 2023-11-15T16:06:01+0000

The formula for getting the arc length is:

$ArcLength=(\theta)/(360)*2\pi r$

where θ = the central angle and r = radius.

Since central angle = 120 and radius = 6cm, let's plug them into the formula above.

$ArcLength=(120)/(360)*2*\pi*6cm$

Then, solve.

$\begin{gathered} ArcLength=(1)/(3)*12cm*\pi \\ ArcLength=12.56637cm \\ ArcLength\approx12.566cm \end{gathered}$

Therefore, the length of Arc BC is approximately 12.566 cm.