Question

Find the radius of a circle if an arc of central angle 40 degree has length of 44 pie cm. Hence, find the area of the sector formed by this arc.

Answer 1

hope it will help you

Answer 2

The area of the sector is 4356π cm².

Step-by-step explanation:

The length of the circumference of a circle is 2πr which is equivalent to a rotation of 360°

So, 40° rotation is equivalent to $\frac{(2\pi r) \times 40 }{360}$ = 0.222πr arc length.

Now, given that 0.222πr = 44π

⇒ r = 198 cm

Now, area of a circle with radius 198 cm is πr² = 39204π cm²

Here, 360° rotational area is 39204π cm².

Hence, 40° rotational area will be $\frac{39204 \times 40}{360} \times \pi = 4356\pi$ cm² (Answer)