Question

The radius of a sector is 21 cm and its central angle is 120 degree find the length of arc and area of a sector

Answer 1

$\sf\large{ \underline{Solution-} }$

Here it is given that,

• Radius of a sector = 21 cm
• Central angle = 120°

➢ We have to find the length of arc and area of a sector.

We know that,

$\boxed{\tt \: Length \: of \: arc \: = \: \sf \dfrac{ \theta}{360 ^ \circ} \times2 \pi r}$

• θ = angle subtended at centre = 120°

So,

$\implies \: \sf \dfrac{ 120^ \circ}{360^ \circ} \times 2 \times \dfrac{22}{7} \times 21$

$\implies \: \sf \dfrac{1}{3} \times 2 \times 22 \times 3$

$\implies \: \sf 2 \times 22$

$\implies \: \sf 44 \: cm$

➢ So, length of arc = 44 cm.

Now,

$\boxed{ \tt Area \: of \: sector \: = \: \sf \dfrac{ \theta}{360^ \circ} \times\pi r^{2}}$

$\implies \: \sf \dfrac{ 120^\circ}{360^ \circ} \times \dfrac{22}{7} \times 21^{2}$

$\implies \: \sf \dfrac{ 120^\circ}{360^ \circ} \times \dfrac{22}{7} \times 21 \times 21$

$\implies \: \sf \dfrac{ 1}{3 } \times 22 \times 21 \times 3$

$\implies \: \sf 22 \times 21$

$\implies \: \sf 462 \: cm^{2}$

➢ So, area of sector = 462 cm²

Answer 2

Answer:

Step-by-step explanation:

Given radius(r)=21cm and the angle(θ)=120

∘

length of arc=r×θ

here r=21cm, θ=120

∘

=

360

120

​

×2π

length of arc =  

360

0

θ

​

×2πr=

360

0

120

0

​

×2×

7

22

​

×21=44cm