Let the radius and height of cone be r and h respectively
![\[Radius\text{ }of\text{ }sphere\text{ }=\text{ }R\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d09fa5670285e7c0dd81ea1a8869da05_l3.png "Rendered by QuickLaTeX.com")
![\[{{R}^{2}}~=\text{ }{{r}^{2}}~+\text{ }{{\left( h\text{ }-\text{ }R \right)}^{2}}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-3b8078f627c5f05a42e526e231033593_l3.png "Rendered by QuickLaTeX.com")
![\[{{R}^{2}}~=\text{ }{{r}^{2}}~+\text{ }{{h}^{2}}~+\text{ }{{R}^{2}}-\text{ }2hR\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-68ce2d15fcc93f5abbf918eacba84bfa_l3.png "Rendered by QuickLaTeX.com")
![\[{{r}^{2}}~=\text{ }2hR\text{ }-\text{ }{{h}^{2}}~\ldots \text{ }\left( 1 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-27fa254d2c6d743fec3f3e6c0d73bdab_l3.png "Rendered by QuickLaTeX.com")
Assuming volume of cone be 
Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3 of the diameter of the sphere.
Show that the cone of the greatest volume which can be inscribed in a given sphere has an altitude equal to 2/3 of the diameter of the sphere.