[tex]\underline{\underline{\large{\red{\mathcal{✒GIVEN:}}}}}[/tex]
A circle with center [tex]\rm{ O }[/tex] and a radius of [tex]\rm{6}[/tex] inches is shown.
[tex]\underline{\underline{\large{\red{\mathcal{REQUIRED:}}}}}[/tex]
Rounded to the nearest tenth of an inch, what is the length of arc [tex]\rm{LMN}[/tex] ?
[tex]\underline{\underline{\large{\red{\mathcal{SOLUTION:}}}}}[/tex]
The length of an arc of a circle, with the central angle provided, is calculated as follows:
[tex]\small{\bm{{ s = length \: of \: an \: arc }} } \\ \boxed{ \bm \red{s = \dfrac{ \theta}{360} \times 2 \pi r}} [/tex]
The variables are:
[tex]\bullet \: \: \tt{r=6}[/tex]
[tex]\bullet \: \: \tt{\theta =270}[/tex]
Now we substitute values and solve as follows:
[tex]\tt{s = \dfrac{270}{360} \times 2 \times 3.14 \times 6}[/tex]
Simplify:
[tex]\tt{s = \dfrac{3}{4} \times 2 \times 3.14 \times 6}[/tex]
Simplify further:
[tex]\tt{s = 28.26}[/tex]
Rounded to the nearest term, we have:
[tex]\large{\tt{\purple{s = 28.3 \: in}}}[/tex]
Final Answer:
[tex]\large{\rm{\purple{arc \: length= 28.3 \: in}}}[/tex]
