If a cone of maximum volume is inscribed in a given sphere, then the ratio of the height of the cone to the diameter of the sphere is `3//4` (b) `1//3` (c) `1//4` (d) `2//3`

Explanation

In `\triangle {AOB}, {AO}^{2}+{AB}^{2}={OB}^{2}`


`\Rightarrow({h}-{R})^{2}+{r}^{2}={R}^{2}`



`\Rightarrow {r}^{2}={R}^{2}-({h}-{R})^{2}`


Volume of cone `=\frac{1}{3} \pi {r}^{2} {~h}`
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