A 70° arc of a circle has a length of 51cm. What is the radius of the circle

Question

asked Jun 25, 2021 158k views

1 Answer

Adarsh Wase · Answer 1 · 2021-06-29T16:21:38+0000

The radius of circle is 41.76 cm

Solution:

Given that, 70° arc of a circle has a length of 51 cm

To find: Radius of circle

The formula for arc length when angle given in degrees is:

$Arc\ Length = 2 \pi r * (\theta)/(360)$

Where,

"r" is the radius of circle and
$\theta$ is the central angle in radians

From given,

Arc length = 51 cm

$\theta$ = 70 degrees

Substituting the values in formula,

$51 = 2 * 3.14 * r * (70)/(360)\\\\51 = 6.28 * r * 0.194\\\\51 = 1.2211r\\\\r = (51)/(1.2211)\\\\r = 41.76$

Thus the radius of circle is 41.76 cm