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.
Solution:
Area of sector having central angle $150^{\circ}==\frac{150^{\circ}}{360^{\circ}} \pi(6)^{2}=\frac{5}{12} \times$ Area of circular disc
Now, Area of sector having central angle 90° : Area of sector having central angle 120° : Area of sector having central angle 150°
$=\frac{90^{\circ}}{360^{\circ}} \pi(6)^{2}: \frac{120^{\circ}}{360^{\circ}} \pi(6)^{2}: \frac{150^{\circ}}{360^{\circ}} \pi(6)^{2}$
$=\frac{1}{4}: \frac{1}{3}: \frac{5}{12}$
$=3: 4: 5$