A 120º sector of a circle of radius 21 cm is bent to form a cone. What is the base radius of the cone?
A
3\(\frac{1}{2}\) cm
B
10\(\frac{1}{2}\) cm
C
14 cm
D
7 cm
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
PQ = circumference of the base of the cone = 2πr
PQ = \(\frac{120}{360}\) × 2πr = \(\frac{120}{360}\) × 2 × \(\frac{22}{7}\) × 21 = 44 cm
∴ 44 = 2πr; 44 = 2 × \(\frac{22}{7}\) × r
44 = \(\frac{44}{7}\) r
r = 7 cm
OR
r = \(\frac{R\theta}{360}\) = \(\frac{21 \times 120}{360}\) = 7cm.
Source: WAEC / JAMB / NECO Classroom Archive (Record #75845)