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Surface Areas and Volumes
CBSE 2026 Board Exam Set 3 (Code 30/1/3)
CBSE_BOARD_PYQ_2026_30_1_3
Grade 10

Question:

[Section C]

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to $1$ 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: Total volume $=$ Volume of cone $+$ Volume of hemisphere $= \dfrac{1}{3}\pi r^2 h + \dfrac{2}{3}\pi r^3$.
$V_{\text{cone}} = \dfrac{1}{3}\pi(1)^2(1) = \dfrac{\pi}{3}$ cm$^3$. $V_{\text{hemisphere}} = \dfrac{2}{3}\pi(1)^3 = \dfrac{2\pi}{3}$ cm$^3$. Total Volume $= \dfrac{\pi}{3} + \dfrac{2\pi}{3} = \pi$ cm$^3$. [3.0 Marks]

Correct Answer: π cm³
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