Question

The radius of the circle in which central angle is 60° intercepts an arc of length 37.4 cm is _____ ( π=22/7)

Answer 1

Given :

Angle ( ϴ)=60°

Length (l)= 37.4 cm

To find:

Radius of the circle= ?

Solution:

$Radian \: measure \: = \frac{\pi}{180} \times degree \: measure \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{\pi}{180°} \times 60° \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{\pi}{3} radians$

We know, r=l/ϴ => [ ϴ is in radians]

$r = \frac{37.4}{ \frac{\pi}{3} } \\ r = \frac{37.4}{ \frac{22}{7 \times 3} } \\ r = 37.4 \times \frac{21}{22} \\ r = 3.4 \times \frac{21}{2} \\ r = \frac{71.4}{2} \\ r = 35.7 \: cm$

Answer 2

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Given,

Length of the arc = l = 37.4 cm

Central angle = θ = 60° = 60π/180 radian = π/3 radians

We know that,

r = l/θ

= (37.4) * (π / 3)

= (37.4) / [22 / 7 * 3]

= 35.7 cm

Hence, the radius of the circle is 35.7 cm

Hope it's Helpful....:)