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=(\theta)/(360^0)*\pi r^2`

Given

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

Therefore,

`234\pi=(\theta)/(360)*\pi(18)^2`

Solve for θ

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

Hence, the answer is

`260^0`