A 120° sector of a circle of radius 21cm is bent to form a cone. What is the base radius of the cone?
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Correct Answer: Option B
Explanation:
The length of the arc subtended by the sector of angle 120° = 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
The length of the arc subtended by the sector of angle 120° = 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