Question

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.

Answer 1

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

$A=\frac{\theta}{360^0}\times\pi r^2$

Given

$\begin{gathered} r=18cm \\ A=234\pi cm^2 \end{gathered}$

Therefore,

$234\pi=\frac{\theta}{360}\times\pi(18)^2$

Solve for θ

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

Hence, the answer is

$260^0$