The volume of a sphere of radius r is:
Aπ r³
B(4/3) π r³
C(2/3) π r³
D4 π r²
Answer & Solution
Correct answer: B. (4/3) π r³
1. The textbook derives the sphere volume by approximating it with small pyramids whose apex is the centre.
2. Sum of pyramid volumes = (1/3) × surface area × radius = (1/3) × 4πr² × r.
3. So volume = (4/3) π r³.
4. 4 π r² is the surface area, not the volume.
5. So the volume formula is (4/3) π r³.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 8-9 (pp 200-219, 2019 ed.)._
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