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Surface Areas and Volumes
RD Sharma
CBSE
Grade 10

Question:

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is:
(a) $1 : 2 : 3$
(b) $2 : 1 : 3$
(c) $3 : 2 : 1$
(d) $1 : 3 : 2$

Step-by-Step Solution

Key Concept: Height $h = r$. Volumes: Cone $= \dfrac{1}{3}\pi r^3$, Hemisphere $= \dfrac{2}{3}\pi r^3$, Cylinder $= \pi r^3$. Ratio $= \dfrac{1}{3} : \dfrac{2}{3} : 1 = 1 : 2 : 3$.
Ratio $= \dfrac{1}{3} : \dfrac{2}{3} : 1 = 1 : 2 : 3$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Evaluating volume ratio $= 1 : 2 : 3$: 1.0 Mark

Correct Answer: $1 : 2 : 3$
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