Question

Ramsay cuts out a piece from a circular cardboard for a school project. The radius of the cardboard is 14 inches and the measure of the central angle is 54 degrees, as shown

Answer 1

Given the figure, we can deduce the following information:

1. The radius of the cardboard is 14 inches.

2. The measure of the central angle is 54 degrees.

To determine the length of the curve boundary of the piece of the cardboard, we use the formula:

$\text{Arc Length}=2\pi r(\frac{\theta}{360})$

where:

θ=central angle

r=radius

We plug in what we know:

$\begin{gathered} \text{Arc Length}=2\pi r(\frac{\theta}{360}) \\ =2\pi(14)(\frac{54}{360}) \\ \text{Simplify} \\ \text{Arc Length}=4.2\pi\text{ inches} \end{gathered}$

Therefore, the answer is 4.2π inches.