I don't understand this.
So we have:
\begin{align}
r &= 12 \color{gray}{\text{ (radius of circle)}} \\
d &= 24 \text{ (r}\times2) \color{gray}{\text{ (diameter of circle)}} \\
c &= 24\pi \text{ (}\pi\times d) \color{gray}{\text{ (circumference of circle)}} \\
a &= 144\pi \text{ (}\pi\times r^2) \color{gray}{\text{ (area of circle)}}
\end{align}
And we have:
\begin{align}
ca &= 60^\circ \color{gray}{\text{ (Central Angle of sector)}} \\
ratio &= \frac{60}{360} = \frac{1}{6} \color{gray}{\text{ (ratio of ca to circle angle which is 360 degrees)}}
\end{align}
So now we can calculate:
\begin{align}
al = \frac{1}{6} \times 24\pi &= 4\pi \color{gray}{\text{ (arc length of SECTOR = ratio X circumference of circle)}}
sa &= \frac{1}{6} \times 144per = 24\pi \color{gray}{\text{ (sector area = ratio X area of circle)}}
\end{align}
So my question is: What is meant by the perimeter of a Sector. Is it the arch length or the are of a Sector? And what is $24 + 4\pi$?
Best Answer
The perimeter of the sector includes the length of the radius $\times 2$, as well as the arc length. So the perimeter is the length "around" the entire sector, the length "around" a slice of pizza, which includes it's edges and its curved arc.
The arc length is just the curved portion of the circumference, the sector permimeter is the length of line $\overline{AC} = r$ plus the length of line $\overline{BC} = r$, plus the length of the arc ${AOC}$.
The circumference of the circle is the total arc length of the circle.
Length is one-dimensional, the length of a line wrapped around the circle. Area is two dimensional; All of what's inside the circle.