A 120^\circ sector of a circle of radius 21cm is bent to form a cone. What is the base radius of the cone?
A
31/2cm
B
7cm
C
1O1/2cm
D
14cm
E
21cm
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
The length of the arc subtended by the sector of angle 120^\circ = circumference of the base of the cone.
\(\frac{120}{360} \times 2 \times \frac{22}{7} \times 21 = 2\pi r\)
\(44 = 2\pi r\)
\(r = 22 \div \pi\)
\(r = 22 \times \frac{7}{22}\)
r = 7 cm
Source: Myschool Past Questions Archive (Record #23746)