Question

find the length of an arc of central angle 40° and radius 4 cm​

Answer 1

Answer:

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}

360

(2πr)×40

= 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

360

39204×40

×π=4356π cm² (