Question

A circular disc of radius 6 cm is divided into three sectors with central angles 90°,120° and 150°. What part of the whole circle is the sector with central angle 150°? Also, calculate the ratio of the areas of the three sectors.

Answer 1

Area of sector having central angle 150° = $=\frac{150°}{360°}\mathrm{\pi }{\left(6\right)}^2=\frac{5}{12}\times \mathrm{Area}\mathrm{of}\mathrm{circular}\mathrm{disc}$

Now, Area of sector having central angle 90° : Area of sector having central angle 120° : Area of sector having central angle 150°
$$\begin{gathered} =\frac{90°}{360°}\mathrm{\pi }{\left(6\right)}^2:\frac{120°}{360°}\mathrm{\pi }{\left(6\right)}^2:\frac{150°}{360°}\mathrm{\pi }{\left(6\right)}^2 \\ =\frac{1}{4}:\frac{1}{3}:\frac{5}{12} \\ =3:4:5 \end{gathered}$$