Question

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 1

Answer:

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

angle = 144°

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

Step-by-step explanation:

$we \: know \: that \: \\ \\ area \: of \: circle \: = \pi {r}^{2} \\ \\ 25\pi = \pi {r}^{2} \\ \\ {r }^{2} = 25 \\ r = 5cm \\ \\ lenth \: of \: arc \: = r \: × angle \\ 5 \times \frac{4\pi}{5} = 4\pi \: cm \\ \\ \\ area \: o \: sctor \: = \frac{1}{2} {r}^{2} agle \\ \frac{1}{2} ×5×5×\frac{4\pi}{5} \\ \\ = 10\pi \: \: sq \: cm$

Answer 2

Step-by-step explanation:

therefore S =4picm,. and A = 10pi sq cm

I hope it is useful