Questions & Answers

Question

Answers

A. 462

B. 460

C. 465

D. 470

Answer
Verified

The area of a sector of the circle is calculated by using the formula:

Area =$\pi {r^2} \times \left( {\dfrac{\theta }{{360^\circ }}} \right)$, where ‘θ’ is the angle subtended at the centre.

Here, according to the question

Radius of the sector = 21 cm

Angle subtended by the arc at centre= θ = 120°

Now, we calculate the area of sector OAB

Area of the sector = $\pi {r^2}\dfrac{\theta }{{360}}$

$\begin{gathered}

= \dfrac{{22}}{7} \times 21 \times 21 \times \dfrac{{120}}{{360}} \\

= \dfrac{{22 \times 21 \times 21}}{{7 \times 3}} \\

= 462c{m^2} \\

\end{gathered} $

Therefore, the area of the sector is 462 $cm^2$

$\theta = \dfrac{l}{r}$, where θ is in radian. Therefore, the area of sector = $A = \dfrac{{\left( {lr} \right)}}{2}$