Question

A semicircle is divided into two sectors whose angles are in ratio 2:3 find the ratio of their areas

Answer 1

Answer:

Ratio of angles = 4:5

Let, angles = 4x and 5x

Ratio of areas:

\begin{gathered}( \frac{4x}{360} \times \pi {r}^{2} ) \div ( \frac{5x}{360} \times \pi {r}^{2} ) \\ \\ = > \frac{4x}{360} \times \pi {r}^{2} \times \frac{360}{5x} \times \frac{1}{\pi {r}^{2} } \\ \\ = > \frac{4}{5} \end{gathered}

(

360

4x

×πr

2

)÷(

360

5x

×πr

2

)

=>

360

4x

×πr

2

×

5x

360

×

πr

2

1

=>

5

4

=> 4:5