Prove that a conical tent of given capacity will require the least amount of canvas when the height is `sqrt(2)` times the radius of the base.

Explanation

Let radius and height be `r` and `h` respectively.

Volume,`V=1/3pir^2h`

`h=frac{3V}{pir^2}`

Surface area,`S=pirsqrt{r^2+({3V}/{pir^2})^2} `

`implies {dS}/{dr}=d/{dr}[ pirsqrt{r^2+({3V}/{pir^2})^2}]`

For minimum value of `S`, `{dS}/{dr}=0`

`implies 3pi^2r^6=pi^2r^6+9V^6`

`implies 2pi^2r^6=9V^6`

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