Question

The area of the circle is 169 sq.cm.find the length of its arc subtending an angle of 78° at the centre also find the area of the corresponding sector.

Answer 1

Step-by-step explanation:

Given: Area of circle

$=\pi r^2 \\</p><p>\therefore 169 = \pi r^2\\</p><p>r^2= \frac{169}{\pi}\\</p><p>r = \sqrt{\frac{169}{\pi}}\\</p><p>r = \frac{13}{\sqrt {\pi}}$

Now, length of arc

$l= \frac{\theta}{360\degree}\times 2\pi r = \frac{78\degree}{360\degree}\times 2\pi\times \frac{13}{\sqrt {\pi}}\\</p><p>l = \frac{13}{60}\times 2 \sqrt {\pi}\times 13\\</p><p>l = \frac{169}{30}\sqrt {\pi}$