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Surface Areas and Volumes
RD Sharma
CBSE
Grade 10

Question:

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to $1\text{ cm}$ and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$.

Step-by-Step Solution

Key Concept: Volume $= \text{Cone Vol} + \text{Hemisphere Vol} = \dfrac{1}{3} \pi (1)^2(1) + \dfrac{2}{3} \pi (1)^3 = \dfrac{\pi}{3} + \dfrac{2\pi}{3} = \pi\text{ cm}^3$.
$\text{Volume} = \dfrac{1}{3}\pi(1) + \dfrac{2}{3}\pi(1) = \pi\text{ cm}^3$. [2.0 Marks]

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🎯 Official CBSE Marking Scheme:
Applying sum of volumes formula and evaluating $= \pi\text{ cm}^3$: 2.0 Marks

Correct Answer:
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