The arc of a circle 50 cm long, subtends angle of 75° at the center of the circle. Find correct to 3 significant figures, the radius of the circle. Take \(\pi = \frac{22}{7}\)
A
8.74cm
B
38.2cm
C
61.2cm
D
76.4cm
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
Length of arc = \(\frac{\theta}{360} \times 2\pi r\)
\(50 = \frac{75}{360} \times 2 \times \frac{22}{7} \times r\)
\(r = \frac{50 \times 360 \times 7}{75 \times 2 \times 22}\)
\(r = \frac{420}{11}\)
= 38.18 cm \(\approxeq\) 38.2 cm (3 sig. figs)
Source: WAEC / JAMB / NECO Classroom Archive (Record #26466)