It is desired to construct a cylindrical vessel of capacity `500 cu m`, open at the top. What should be the dimensions of the vessel so that the material used is minimum, given that the thickness of the material used is `2 cm`?

A cylindrical vessel of capacity 500 cubic metres open at the top is to be constructed. Find the dimensions of the vessel if the material used is minimum given that the thickness of the material used is 2 cm.

If a cylindrical vessel of given volume V with non lid on the top is to be made from a sheet of metal, then the radius (r) and height (h) of the vessel so that the metal sheet used is minimum is

A right cylindrical vessel of a given capacity is formed using least possible material.Then the ratio of the height to the radius of the base is

A rectangular page is to contain 24cm^(2) of print. The margins at the top and bottom of the page are 1.5 cm and the margins at other sides of the page is 1 cm. What should be the dimensions of the page so that the area of the paper used is minimum.

Two transparent slabs having equal thickness but different refractive indices mu_1 and mu_2 , are pasted side by side to form a composite slab. This slab is placed just after the double slit in a Young's experiment so that the light from one slit goes through one material and the light from the other slit goes through the other material. What should be the minimum thickness of the slab so that there is a minimum at the point P_0 which is equidistant from the slits ?

A lipuid is poured into a cylindrical vessel of height H and mass M. to what height a liquid of density p should be poured so that the centre of gravity of the vessel + kuqyud ' sustem mat be at the minimum height from the bottom . Negalect the mass of the bottom .the area of cross - section of the vessel of A .