Question

The area of a circle is 2571 sq.cm. Find
the length of its are subtending an angle
of 144º at the centre. Also find the area
of the corresponding sector.​

Answer 1

Answer:

given:- Area of circle = 55 pie sq.cm.

angle = 144°

144 \times \frac{\pi}{180} = \frac{4\pi}{5}144×

180

π

=

5

4π

Step-by-step explanation:

\begin{gathered}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\end{gathered}

weknowthat

areaofcircle=πr

2

25π=πr

2

r

2

=25

r=5cm

lenthofarc=r×angle

5×

5

4π

=4πcm

areaosctor=

2

1

r

2

agle

2

1

×5×5×

5

4π

=10πsqcm

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