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When a sector of central angle 45° is cut from a circle of radius 12 cm and rolled into a cone, the base radius of the cone equals:
Answer & Solution
Correct answer: A.
1. The arc length of the sector becomes the circumference of the cone's base.
2. 45° is 1/8 of 360°, so the arc length is 1/8 of the full circle's circumference.
3. The cone's base circumference is therefore 1/8 of (2π × 12) = 2π × 1.5.
4. Equating to 2πr_base, the base radius is 12 × (1/8) = 1.5 cm.
5. So the base radius equals 1.5 cm.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7-8 (pp 180-199, 2019 ed.)._
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