Rosasmark515idn
Answered

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1. The diagram shows a sector of a circle. The area of the sector is 180m2. Find the value of O in terms of pi. 9m​

Sagot :

UK2019idn

✏️CIRCLE

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[tex]\underline{\mathbb{PROBLEM:}}[/tex]

  • The area of the sector is 180m². Find the value of [tex] \theta[/tex] in terms of pi with the radius is 9m.

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\underline{\mathbb{ANSWER:}}[/tex]

[tex] \qquad \LARGE \rm» \: \: \green{\theta = 800\pi\degree} [/tex]

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

[tex]\underline{\mathbb{SOLUTION:}}[/tex]

- By Using the formula, find the central angle of the circle with the sector area is 180m² and the radius is 9m.

[tex]\begin{aligned}&\bold{\color{lightblue}Formula:}\\&\boxed{A_{sec} = \frac{ \theta}{360 \degree} \cdot \pi {r}^{2} }\end{aligned} [/tex]

  • [tex]\begin{aligned}{180 {m}^{2} = \frac{ \theta}{360 \degree} \cdot \pi(9m)^{2} }\end{aligned} [/tex]

  • [tex]\begin{aligned}{180 {m}^{2} = \frac{ \theta}{360 \degree} \cdot \pi(81 {m}^{2} ) }\end{aligned} [/tex]

  • [tex]\begin{aligned}{180 {m}^{2}(360) = \frac{ \theta}{ \cancel{360 \degree}} \cdot \pi(81 {m}^{2} ) \cancel{(360)} }\end{aligned} [/tex]

  • [tex]64800 {m}^{2} = \theta \cdot81{m}^{2} \pi[/tex]

  • [tex]64800 {m}^{2} =81{m}^{2} \pi \theta[/tex]

  • [tex] \frac{64800 \cancel{{m}^{2}}}{81 \cancel{{m}^{2}} \pi} = \frac{ \cancel{81{m}^{2} \pi }\theta}{ \cancel{81{m}^{2} \pi}} \\ [/tex]

  • [tex]800\pi = \theta [/tex]

[tex]\therefore[/tex] The central angle of the circle is 800π degrees.

[tex]\red{••••••••••••••••••••••••••••••••••••••••••••••••••}[/tex]

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