[tex]\large\underline{\rm{PROBLEM}:}[/tex]
- What is the area of the sector of a circle if it has a radius of 8cm and an arc measure of 600°?
[tex]\tt\color{red}{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]
[tex]\large\underline{\rm{ANSWER}:}[/tex]
- [tex]\large\bold{A \: = \: 335.10 \: {cm}^{2} }[/tex]
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[tex]\large\underline{\rm{GIVEN}:}[/tex]
- [tex]\small\bold{Radius(R) \: = \: 8cm}[/tex]
- [tex]\small\bold{ARC \: = \: 600°}[/tex]
[tex]\tt\color{red}{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]
[tex]\large\underline{\rm{FORMULA}:}[/tex]
➢ To find the area of the sector, here's the formula that we could use.
- [tex]\small\bold{A \: = \: } \frac{600°}{360°} \: \times \: \pi {r}^{2} \\ [/tex]
[tex]\tt\color{red}{\overline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}[/tex]
[tex]\large\underline{\rm{SOLUTION}:}[/tex]
➢ To find the area of the sector, the first we need to do is divide the ARC to 360°.
- [tex]\small\bold{A \: = \: } \frac{600°}{360°} \: \times \: \pi {r}^{2} \\ [/tex]
- [tex]\small\bold{A \: = \: } \frac{5}{3} \: \times \: \pi {r}^{2} \\ [/tex]
- [tex]\small\bold{A \: = \: } \frac{5}{3} \: \times \: \pi \: \times \: 8 {\small\bold{cm}}^{2} \\ [/tex]
- [tex]\small\bold\color{green}{A \: = \: 335.10 {cm}^{2}}[/tex]
⟹ Therefore, the area of a circle will be, [tex]\small\bold{335.10 {cm}^{2}}[/tex]
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[tex]\tiny\bold\color{olive}{{\tt{\colorbox{black}{CarryOnLearning:)}}}}[/tex]
