Q.A semicircle is divided into two sectors whose angles are in the ratio 4:5. Find the ratio of their areas?
A) 5:1 B) 4:5 C) 5:4 D) 3:4

Step 1: Both sectors come from the same semicircle, so they share the same radius $r$. Sector area $=\frac12 r^2\theta$ is then directly proportional to $\theta$ alone. …

Recognise that equal-radius sectors have area proportional to their central angle, so the area ra …

• Inverting the ratio (writing 5:4 instead of 4:5).
• Trying to compute each angle's actual value (4/9×180°, 5/9×180°) unnecessarily, when the ratio itsel …