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The volume of the largest cone that can be inscribed in a sphere of radius $= 6 c m$ is

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$\frac{32}{3} π c . c$

$172 π c . c$

$\frac{256}{3} π c . c$

$\frac{288}{3} π c . c$

answer is C.

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Detailed Solution

$R = 6 c m$

$v = \frac{8}{27} v o l u m e = \frac{8}{27} \times \frac{4}{3} π R^{3}$

$= \frac{32}{81} \times π \times 6 \times 6 \times 6$

$= \frac{256}{3} π c . c$

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