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)).

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)). (A) 37.5 cm (B) 32.8 cm (C) 35.7 cm (D) 34.5 cm

Tardigrade Admin · Accepted Answer

Here l=37.4 cm and θ=60°=(60π/180) radian =(π/3) Hence, by r=(l/θ), we have r=(37.4 × 3/π)=(37.4 × 3 × 7/22) =35.7 cm

Q. Find the radius of the circle in which a central angle of $6 0^{\circ}$ intercepts an arc of length $37.4 c m$ (use $π = \frac{22}{7}$ ).

$37.5 c m$

$32.8 c m$

$35.7 c m$

$34.5 c m$

Here $l = 37.4 c m$ and $θ = 6 0^{\circ} = \frac{60 π}{180}$ radian $= \frac{π}{3}$
Hence, by $r = \frac{l}{θ}$ , we have
$r = \frac{37.4 \times 3}{π} = \frac{37.4 \times 3 \times 7}{22}$
$= 35.7 c m$

Q. Find the radius of the circle in which a central angle of 60∘ intercepts an arc of length 37.4cm (use π=722​).

37.5cm

32.8cm

35.7cm

34.5cm