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Surface Areas and Volumes
RD Sharma
CBSE
Grade 10

Question:

A solid sphere of radius $r$ is melted and recast into the shape of a solid cone of height $r$. Find the radius of the base of the cone. (Note: standard ratio formula).

Step-by-Step Solution

Key Concept: $\dfrac{4}{3} \pi r^3 = \dfrac{1}{3} \pi R^2 (r) \Rightarrow R^2 = 4 r^2 \Rightarrow R = 2r$.
$\dfrac{4}{3} \pi r^3 = \dfrac{1}{3} \pi R^2 r \Rightarrow R^2 = 4 r^2$. [1.0 Mark]
$R = 2r$. The base radius of the cone is $2r$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Equating volume formulas: 1.0 Mark
Solving base radius $R = 2r$: 1.0 Mark

Correct Answer:
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