# An open tank is to be constructrd  with a square base and vertical sides so as to contain a given quantity of water.Show that the expenses of lining with lead will be least if depth is made half of width.

Arun Kumar IIT Delhi
8 years ago
Hi

$\\base dimension a=a \\hieght =h \\=>v=a^2h=c=>d(a^2h)/da=0 \\=>2ah+a^2dh/da=0 \\=>{dh \over da}={-2h \over a} \\=>s=a^2+4ah \\=>{ds \over da}=0=2a+4a{dh \over da}+4a=0 \\=>2a+4h+4a*{-2h \over a}=0 \\=>2a=4h=>h=a/2$
Thanks & Regards, Arun Kumar, Btech,IIT Delhi, Askiitians Faculty