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A 120º sector of a circle of radius 21 cm is bent to form a cone....

Mathematics
WAEC 2025

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
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Correct Answer: Option D
Explanation

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.


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WAEC offline past questions - with all answers and explanations in one app - Download for free
Post UTME Past Questions Agent
Post-UTME Past Questions - Original materials are available here - Download PDF for your school of choice + 1 year SMS alerts
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