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From a solid sphere of radius 10 cm a cone of height 16 cm is carved out (apex on the surface, axis through the centre, base inside). The fraction of the sphere's volume taken up by the cone is approximately:
Answer & Solution
Correct answer: B.
1. The cone has its apex on the sphere and base perpendicular to the diameter through the apex.
2. Geometric setup gives base radius = √(r² − (r − h_cone_distance)²) — for height 16 from apex along a diameter of 20, the base lies 16 from the apex on the diameter, leaving 4 above the centre and so base radius = √(10² − (16 − 10)²) = √(100 − 36) = 8.
3. Cone volume = (1/3) π × 8² × 16 = (1024/3) π.
4. Sphere volume = (4/3) π × 1000 = (4000/3) π.
5. Ratio = 1024 / 4000 = 0.256, closest to 3/10.
_Source: SCERT Kerala Std X Mathematics Part-2, Chapter 8-9 (pp 200-219, 2019 ed.)._
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