Question

The length of an Arc of a circle with radius 12 cm is 10 cm find the central angle of this Arc

Answer 1

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Answer 2

Concept:

The distance along the curved line that makes up the arc is measured using the arc length formula (a segment of a circle). The arc length is, to put it simply, the distance that passes through the curved line of the circle that forms the arc. It should be noted that the arc's length is greater than the separation of its ends along a straight line.

Given:

Length of arc, l = 10 cm

Radius, r = 12 cm

Find:

We have to find the central angle of this arc.

Solution:

As we know that the formula of central arc,

$\theta$/360° x 2r = l

By putting the value l = 10 cm and r = 12 cm, we get:

$\theta$/360° x 2 x 22/7 x 12 = 10

$\theta$ = 10 x 360° x 1/2 x 7/22 x 1/12

$\theta$ = 25200/528

$\theta$ = 47.72°.

Hence, the central angle of this arc, $\theta$ = 47.72°.

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