Question

Ramsay cuts out a piece from a circular cardboard for a school project. The radius of the cardboard is 10inches and the measure of the central angle is 49 degrees, as shown.x inyoWhat is the length of the curved boundary of the piece of the cardboard Ramsay cuts out?

Answer 1

The formula to find the arc length of a circle is:

`\begin{gathered} \text{arc length }=(\theta)/(360\degree)\cdot2\pi r \\ \text{ Where} \\ \theta\text{ is the measure of the central angle} \\ r\text{ is the radius of the circle } \end{gathered}`

In this case, we have:

`\begin{gathered} \theta=49\degree \\ r=10in \\ \text{arc length }=(\theta)/(360\degree)\cdot2\pi r \\ \text{arc length }=(49\degree)/(360\degree)\cdot2\pi(10in) \\ \text{arc length }=(49)/(360)\cdot2\pi\cdot10in \\ \text{arc length }=(49\cdot2\cdot10)/(360)\pi in \\ \text{arc length }=(49\cdot2\cdot10)/(18\cdot2\cdot10)\pi in \\ \text{arc length }=(49)/(18)\pi in \\ \text{ or} \\ \text{arc length }\approx2.72\pi in\Rightarrow\text{ The symbol }\approx\text{ is read 'approximately'.} \end{gathered}`

Therefore, the length of the curved boundary of the piece of the cardboard Ramsay cuts out is

`\begin{gathered} (49)/(18)\pi\text{ inches} \\ \text{ or} \\ 2.72\pi\text{ inches} \end{gathered}`