An open box with a square base is to be made out of a given Iron sheet of area 36 square meter. Show that the maximum volume of the box is `12sqrt3` cubic meter.

An open box with a square base is to be made out of a given Iron sheet of area 18 square meter. Show that the maximum volume of the box is 3sqrt6 cubic meter.

An open box with a square base is to be made out of a given Iron sheet of area 27 square meter. Show that the maximum volume of the box is 13.5 cubic meter.

An open box with a square base is to be made out of a given iron sheet of area c^2 square units. Show that the maximum volume of the box is c^3/(6sqrt3) cubic units.

An open box with a square base is to be made out of a given iron sheet of area 27sq.m. Show that the maximum volume of the box is 13.5 cu. Cm.

An open tank with a square base and vertical sides is to be constructed from a metal sheet so as to hold a given quantity of water. Show that the cost of the material will be least when the depth of the tank is half of its width.

A square sheet of tin of side 36 cm is to be made into a box without top by cutting off squares from each comer and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is maximum ?

A square sheet of tin whose side is 18 cm to be made into a box without top by cutting off squares from each comer and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is maximum ?