Question

Find the area of the sector and the length of the arc if angle subtended by
the arc of the sector at the center is 60° and radius of the circle is 14 cm.​

Answer 1

Step-by-step explanation:

Length of arc = α/360 × 2πr

Area of sector = α/360 × πr²

Here, α = 60°

r = 14 cm

Length of arc =

$\frac{ \alpha }{360} \times 2\pi \times r \\ = \frac{60}{360} \times 2 \times \frac{22}{7} \times 14 \\ = \frac{1}{6} \times 2 \times 22 \times 2 \\ = \frac{44}{3} = 14.66 \: cm$

Area of sector =

$\frac{ \alpha }{360} \times \pi \times {r}^{2} \\ = \frac{60}{360} \times \frac{22}{7} \times 14 \times 14 \\ = \frac{1}{6} \times 22 \times 2 \times 14 \\ = \frac{1}{3} \times 22 \times 14 \\ = 102.66 \: {cm}^{2}$

Answer 2

Step-by-step explanation:

Length of arc = α/360 × 2πr

Area of sector = α/360 × πr²

Here, α = 60°

r = 14 cm

Length of arc =

\begin{gathered} \frac{ \alpha }{360} \times 2\pi \times r \\ = \frac{60}{360} \times 2 \times \frac{22}{7} \times 14 \\ = \frac{1}{6} \times 2 \times 22 \times 2 \\ = \frac{44}{3} = 14.66 \: cm\end{gathered}

360

α

×2π×r

=

360

60

×2×

7

22

×14

=

6

1

×2×22×2

=

3

44

=14.66cm