Question

$Assertion:$ In a circle of radius $6cm$, the angle of a sector is $60°$. Then the area of the sector is $18\frac{6}{7}c{m}^2.$
$Reason:$ Area of the circle with radius $r$ is $\pi r^2$.

Answer 1

Option (B) is the right answer.

Radius of the circle = 6 cm.
Also, angle of the sector = 60°
So,
Area of the sector = $\frac{\theta }{360°}\times (\pi \times r^2)$
$=\frac{60°}{360°}\times (\pi \times 6^2)$
= (⅙) × ( π × 6 × 6)
= (132/7)
$=18\frac{6}{7}c{m}^2.$
Therefore, the given assertion is true.
We know, area of circle is equal to $\pi r^2$, but by using this formula, we can’t find the given area of the sector.
Therefore, it is not the correct explanation of the given assertion.