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In the textbook's derivation of the sphere surface area, the sphere is shown to have the same curved surface as a cylinder whose:
ARadius equals the sphere's radius and height equals the sphere's radius
BRadius equals the sphere's diameter and height equals the sphere's radius
CRadius is twice the sphere's radius and height equals the sphere's diameter
DRadius equals the sphere's radius and height equals the sphere's diameter
Answer & Solution
Correct answer: D. Radius equals the sphere's radius and height equals the sphere's diameter
1. The derivation approximates the sphere by a stack of frustums and matches each frustum's curved area to a cylinder.
2. The full approximating cylinder has base radius equal to the sphere's radius r.
3. Its height equals 2r — that is, the sphere's diameter.
4. The cylinder's curved surface area is 2π × r × 2r = 4πr², equal to the sphere's surface area.
5. So the matching cylinder has radius r and height 2r.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 8-9 (pp 200-219, 2019 ed.)._
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