Question

What is the ratio of the area of sector ABC to the area of sector DBE?

I am not quite sure how to do this. So far, since there are variables instead of numbers, I have got (pi)(r)^2:(pi)(3r)^2, but I know that is definitely wrong.

Answer 1

4/3

Explanation:

Answer 2

`\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}\qquad \begin{cases} \theta =\textit{angle in degrees}\\ r=radius \end{cases}\\\\ -------------------------------\\\\`


`\bf \cfrac{\triangleleft ABC}{\triangleleft DBE}\qquad \cfrac{(\beta \pi (2r)^2)/(360)}{(3\beta \pi (r)^2)/(360)}\implies \cfrac{\beta \pi (2r)^2}{360}\cdot \cfrac{360}{3\beta \pi (r)^2}\implies \cfrac{\beta \pi 2^2r^2}{360}\cdot \cfrac{360}{3\beta \pi r^2} \\\\\\ \cfrac{\beta \pi 4r^2}{3\beta \pi r^2}\implies \cfrac{4}{3}`