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Surface Areas and Volumes
NCERT Exemplar
CBSE
Grade 10

Question:

If the slant height of a cone is $13\text{ cm}$ and its base radius is $5\text{ cm}$, then its height is:
(a) $12\text{ cm}$
(b) $8\text{ cm}$
(c) $18\text{ cm}$
(d) $10\text{ cm}$

Step-by-Step Solution

Key Concept: Height $h = \sqrt{l^2 - r^2} = \sqrt{13^2 - 5^2} = 12\text{ cm}$.
$h = \sqrt{169 - 25} = \sqrt{144} = 12\text{ cm}$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Applying Pythagoras to find height $= 12\text{ cm}$: 1.0 Mark

Correct Answer: $12\text{ cm}$
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