Question

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

Answer 1

Question :

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

To find :

The radius of the circle

Solution :

Length = 37.4 cm

$\sf \small \theta = 60 \degree = \frac{\pi}{3} rad$

$\sf \small But \: r = \frac{1}{ \theta}$

$\sf \small= \frac{37.4 \times 3}{\pi}$

$\sf \small= \frac{34.4 \times 3 \times 7}{22}$

$\sf \small= 35.7 \: cm$

Final Answer :

$\frak{So \: the \: answer \: is \: \: \: \underline{ \boxed{ \frak{35.7 \: cm}}}}$

Answer 2

Step-by-step explanation:

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