Question

find the radius of the circle in which a central angle of 60° intercepts an arc of lenght 37.4cm.(use π =22/7

Answer 1

let the radius of circle be "r"

central angle(¥) =60° = π/ 3 radiant

arc length (l) = 37.4

we know from formula...

central angle (¥) = arc length(l) ÷ radius

=). π/3 = 37.4 / r

=). r = 37.4 ×3 /π = 112.2 / π cm

=). r = 112.2 ×7/ 22 = 35.7 cm ans

Answer 2

The answer is 35.7 cm.

Given:

The central angle of an arc is 60°

The length of the arc is 37.4 cm

$\pi = \frac{22}{7}$

To Find:

The radius of the circle

Solution:

The length of an arc with a central angle θ in radians is given as

$l= r\theta$

where r is the radius of the circle.

We will convert the given angle to radians.

$\theta = \frac{60}{180} *\pi=\frac{/pi}{3}\\ \\\theta =\frac{22}{21}$

Therefore

$r= 37.4*\frac{21}{22}\\ \\r=35.7 cm$

The radius of the circle is 35.7 cm.

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