Hello!
First, let's write some important information:
• arch length,: s
,
• area of the sector,: A
,
• central angle θ,: π/12 rad
,
• radius r,: 55.8cm
To obtain the area of sector A, we must use the formula below:
[tex]A=\frac{r^2\cdot\theta}{2}[/tex]
As we know some values, let's replace them:
[tex]A=\frac{55.8^2\cdot\frac{\pi}{12}}{2}=\frac{3113.64\cdot\frac{\pi}{12}}{2}=\frac{\frac{3113.64\pi}{12}}{2}=\frac{259.47\pi}{2}=129.735\pi[/tex]
To finish, we must replace the value of π and solve the multiplication:
Note: I'll consider π = 3.1415 (approximated value).
[tex]\begin{gathered} A=129.735\cdot\pi \\ A=129.735\cdot3.1415 \\ A\cong407.56 \end{gathered}[/tex]
The most approximated answer is alternative A. 407.575cm².
