Question

Class 10 - Area of a sector of central angle 75 degrees of a circle is 770 cm2. Find the length of the corresponding arc of this sector.

Answer 1

Step-by-step explanation:

Given−

OAPBisasectorwithcentralangle=∠AOB=θ=200

o

and

ar.sector=770cm

2

.

Tofindout−

ThelengthofthearcAPB=l=?

Solution−

Lettheradiusofthesectorber.

Thenar.sector=

360

o

θ

×π×r

2

=

360

o

200

o

×

7

22

×r

2

=770

⟹r=

770×

200

o

360

o

×

22

7

cm=21cm.

∴ThelengthofthearcAPB=l=

360

o

θ

×2×π×r

=

360

o

200

o

×2×

7

22

×21cm=

3

220

cm=73

3

1

cm