What is the area of a sector of a circle of radius 21 cm with central angle 270°? (Take \(\pi=\frac{22}{7}\))
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 1039.5 cm2
A sector with central angle \(\theta\) is the fraction \(\displaystyle \frac{\theta}{360^\circ}\) of the whole circle, so its area is \(\displaystyle \frac{\theta}{360^\circ}\times\pi r^2\).
Area of the whole circle \(\displaystyle =\frac{22}{7}\times21\times21=1386\) cm2
Fraction \(\displaystyle =\frac{270^\circ}{360^\circ}=\frac{3}{4}\)
Area of the sector \(\displaystyle =\frac{3}{4}\times1386=1039.5\) cm2
