The area of a circle is 25π sq.cm. Find
the length of its arc subtending an angle
of 144o
at the centre. Also find the area
of the corresponding sector.
Answers
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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Answer:
the area of a circle is 25π sq.cm.Find the length of its arc subtending an angle of 144° at the center. Also find the area of the corresponding sector
Answer:
given:- Area of circle = 55 pie sq.cm.
angle = 144°
144 \times \frac{\pi}{180} = \frac{4\pi}{5}
Step-by-step explanation:
we \: know \: that \: \\ \\ area \: of \: circle \: = \pi {r}^{2} \\ \\ 25\pi = \pi {r}^{2} \\ \\ {r }^{2} = 25 \\ r = 5cm \\ \\ lenth \: of \: arc \: = r \: × angle \\ 5 \times \frac{4\pi}{5} = 4\pi \: cm \\ \\ \\ area \: o \: sctor \: = \frac{1}{2} {r}^{2} agle \\ \frac{1}{2} ×5×5×\frac{4\pi}{5} \\ \\ = 10\pi \: \: sq \: cm
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