Question

find the length of arc abc. use 3.14 for the value of π. round to the nearest hundredth of a cm.

Explanation:

Step1: Calculate the circumference of the circle

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(r = 32\) cm and \(\pi=3.14\), we have \(C=2\times3.14\times32= 200.96\) cm.

Step2: Find the length of arc \(ABC\)

The central angle of arc \(ABC\) is \(270^{\circ}\) (since \(360 - 90=270\)). The formula for the length of an arc is \(L=\frac{\theta}{360}\times C\), where \(\theta\) is the central angle. Substituting \(\theta = 270^{\circ}\) and \(C = 200.96\) cm, we get \(L=\frac{270}{360}\times200.96=\frac{3}{4}\times200.96 = 150.72\) cm.

Answer:

\(150.72\) cm