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Two spheres have volumes in the ratio 27 : 64. The ratio of their radii is:
A1 : 2
B9 : 16
C27 : 64
D3 : 4
Answer & Solution
Correct answer: D. 3 : 4
1. Volume ratio is the cube of the radius ratio because V ∝ r³.
2. So (r₁/r₂)³ = 27/64, giving r₁/r₂ = 3/4.
3. Hence the radii are in the ratio 3 : 4.
4. 9 : 16 would be the surface area ratio (square of radius ratio).
5. So the radii ratio is 3 : 4.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 8-9 (pp 200-219, 2019 ed.)._
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