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A sector with a radius \maroonD{18\,\text{cm}}18cmstart color #ca337c, 18, start text, c, m, end text, end color #ca337c has an area of \goldE{234\pi\,\text{cm}^2}234πcm 2 start color #a75a05, 234, pi, start text, c, m, end text, squared, end color #a75a05.

A Sector With A Radius MaroonD18textcm18cmstart Color Ca337c 18 Start Text C M End Text End Color Ca337c Has An Area Of GoldE234pitextcm2234πcm 2 Start Color A7 class=

Answer :

The formula for the area (A) of the sector is,

[tex]A=\frac{\theta}{360^0}\times\pi r^2[/tex]

Given

[tex]\begin{gathered} r=18cm \\ A=234\pi cm^2 \end{gathered}[/tex]

Therefore,

[tex]234\pi=\frac{\theta}{360}\times\pi(18)^2[/tex]

Solve for θ

[tex]\begin{gathered} \frac{θ}{360}\pi \left(18\right)^2=234\pi \\ \frac{9\pi θ}{10}=234\pi \\ \frac{10\times \:9\pi θ}{10}=10\times \:234\pi \\ 9\pi θ=2340\pi \\ \mathrm{Divide\:both\:sides\:by\:}9\pi \\ \frac{9\pi θ}{9\pi }=\frac{2340\pi }{9\pi } \\ \thereforeθ=260^0 \end{gathered}[/tex]

Hence, the answer is

[tex]260^0[/tex]

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