The volume of the largest right circular cone that can be cut out of a cube of edge $a$ is:
(a) $\dfrac{\pi a^3}{12}$
(b) $\dfrac{\pi a^3}{4}$
(c) $\dfrac{\pi a^3}{3}$
(d) $\dfrac{\pi a^3}{6}$
Step-by-Step Solution
Key Concept: Cone base diameter $= a \Rightarrow r = a/2$, Height $h = a$. Volume $= \dfrac{1}{3} \pi (a/2)^2 (a) = \dfrac{\pi a^3}{12}$.
$V = \dfrac{1}{3} \pi \left(\dfrac{a}{2}\right)^2 (a) = \dfrac{\pi a^3}{12}$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating volume $= \pi a^3 / 12$: 1.0 Mark
Correct Answer: $\dfrac{\pi a^3}{12}$