Question

Which proportion would use to find the area of the sector given the below figure

Answer 1

Explanation

From the question, we are given that

$\begin{gathered} \bar{AC}=radius(r)=7 \\ \angle C=\theta=80^0 \end{gathered}$

If the area of a sector is denoted by x, recall that its formula can be expressed as;

$\begin{gathered} x=\frac{\theta}{360}\times\pi r^2 \\ \therefore\frac{\theta}{360}=\frac{x}{\pi r^2} \end{gathered}$

We can then substitute the parameters into the above formula.

$\begin{gathered} \frac{80}{360}=\frac{x}{\pi7^2} \\ \Rightarrow\frac{80}{360}=\frac{x}{49\pi^{}} \end{gathered}$

Answer:

$\frac{80}{360}=\frac{x}{49\pi^{}}$