Question

If r = 21 cm, ϴ = 120 degree, then find the length of the arc,

A22 cm

B33 cm

C44 m

D55 m

​

Answer 1

Answer:

44 cm is the correct answer

this is how I got

HOPE YOU UNDERSTOOD THE ANSWER

Answer 2

AnswEr:-

Your Answer Is C) 44 cm.

ExplanaTion:-

Given:-

• $\tt\theta$ = 120°.

• Radius (r) = 21 cm.

To Find:-

• The length of arc.

FormulaUsed:-

$\tt\longrightarrow \theta = \dfrac{l}{r} .$

Where,

• $\theta$ is the central angle of arc in radians.

• l = Length of the arc.

• r = Radius of the arc.

So Here,

ϴ is given in degrees so first of all we have to conver it into radians.

And we know that,

$\tt\mapsto \pi \: \: \: radians = 180 \degree$

$\tt\mapsto1\degree = \dfrac{ \pi}{180} \: \: rd.$

$\tt\mapsto1\degree \times120\degree = \dfrac{ \pi}{\cancel{180}} \times \cancel{120} \: \: rd.$

$\tt\mapsto120\degree = \dfrac{ \pi}{3} \times 2 \: \: rd.$

$\tt\mapsto120\degree = \dfrac{2 \pi}{3} \: \: rd.$

$\tt\mapsto120\degree = \dfrac{ 2 \times22 }{7 \times 3} \: \: rd... \:(1).$

Now,

By putting the above values in formual we get,

$\tt\mapsto \theta = \dfrac{l}{r} .$

$\tt\mapsto l = \theta \times r.$

$\tt\mapsto l = \dfrac{2 \times 22}{ 7 \times 3} \times 21 \: cm.$

$\tt\mapsto l = \dfrac{2 \times 22}{ \cancel{21}} \times \cancel{21} \:cm.$

$\tt\mapsto l = 44 \times 1 \: cm.$

$\bf\mapsto{ \boxed{ \bf l = 44 \: cm.}}$

$\bf\therefore$ The Required Length of arc is 44 cm.

So Option C is the final Answer.