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A sphere is fitted inside a cylinder whose base radius equals the sphere's radius and whose height equals the sphere's diameter. The ratio of their surface areas (cylinder : sphere) is:
Answer & Solution
Correct answer: A.
1. Cylinder surface area (with both bases) = 2πr × 2r + 2 × πr² = 4πr² + 2πr² = 6πr².
2. Sphere surface area = 4πr².
3. Ratio = 6πr² : 4πr² = 3 : 2.
4. So the surface area ratio cylinder-to-sphere is 3 : 2.
5. The same 3 : 2 ratio also holds for their volumes.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 8-9 (pp 200-219, 2019 ed.)._
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