Question

length of Arc is 6 π and radius is 6 cm find the central. angle ​

Answer 1

Answer:

The area of sector is 36 cm²

Step-by-step explanation:

Given the radius of Circle 6 cm

The length of arc is given by :-

$\sf \leadsto \frac{x}{360} \times 2\pi r$

where x is angle subtended by an arc at the center of the circle

The length is 12

According to the question,

$\sf \leadsto \: \frac {x}{360} \times2 \times \frac{22}{7} \times {6} = 12 \\ \sf \leadsto \: \frac{x}{360} \times \frac{22}{7} = \frac{12}{2 \times 6} \\ \sf \leadsto \: \frac{x}{360} \times \frac{22}{7} = .........(i)$

The area of sector is given by,

$\sf \leadsto \frac{x}{360} \pi {r}^{2}$

$\sf \leadsto \frac{x}{360} \pi {r}^{2} \\ \rm \: from \: eq. \: (i)\\ \sf \leadsto \frac{x}{360} \times \frac{22}{7} \times 6 \times 6 \\ \sf \leadsto 1 \times 6 \times 6 = {36cm}^{2}$

So, the area of sector is 36 cm²