A sector of a circle of radius 12 cm with an angle of 120° is folded without overlap into a hollow cone. Find the base radius of the cone formed.
Answer and explanation
Correct answer: A. 4 cm
- Step 1: The slant height of the cone L equals the sector radius: L = 12 cm. Step 2. The arc length of the sector becomes the circumference of the cone's base: (θ / 360°) × 2π L = 2π r_base. Step 3. (120° / 360°) × L = r_base => (1/3) × 12 = r_base => r_base = 4 cm. Answer: 4 cm. Why not the others: 6 cm assumes θ = 180°; 3 cm assumes θ = 90°; 8 cm assumes θ = 240°.
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