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A metal sphere of radius 12 cm is melted and recast into 27 small spheres of equal size. The radius of each small sphere equals:
A1 cm
B4 cm
C2 cm
D6 cm
Answer & Solution
Correct answer: B. 4 cm
1. Conservation of volume: 27 × (4/3) π r³ = (4/3) π × 12³.
2. So 27 r³ = 12³.
3. r³ = 12³ / 27 = (12/3)³ = 4³.
4. Hence r = 4 cm.
5. So each small sphere has radius 4 cm.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 8-9 (pp 200-219, 2019 ed.)._
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