Question

the area of the circle is 25 pie sq.cm . the area of the sector formed by an arc subtending an angle of 144 degree at the centre is ??

Answer 1

Answer:

As we know that area of circle (A) is given by-

A=πr

2

Given that:-

Area of circle =25πcm

2

∴πr

2

=25π

⇒r=

25

=5cm

As we know that length of subtending arc (l) is-

l=rθ

where θ is the angle subtended by the arc

Given that tha angle subtended by the arc is 144°

θ=144°=144°×

180°

π

=

5

4π

∴l=5×

5

4π

=4πcm

As Area of sector =

2

1

×r×l

∴ Area of corresponding sector =

2

1

×5×4π=10πcm

2

Hence the length of subtending arc is 4πcm and the area of corresponding sector is 10πcm

2

.

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