Of all the closed cylindrical cans (right circular), which enclose a given volume of 100 cm3, which has the minimum surface area?

Explanation

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

`V=pir^2h`

`h=frac{100}{pir^2}`

Surface area,`S=2pir^2+2pirh=2pir^2+{200}/r`

`implies {dS}/{dr}=4pir-{200}/{r^2}`

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

`implies 4pir-{200}/{r^2}=0`

`implies 4pir^3=200`

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