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 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 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 27 square meter. Show that the maximum volume of the box is 13.5 cubic meter.

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.

The area in square units of the region bounded by y^2=9x and y=3x is:

A pyramid with vertex at point P has a regular hexagonal base ABCDEF. Position vectors of points A and B are hati and hati+ 2hatj , respectively. The centre of the base has the position vector hati+hatj+sqrt3hatk . Altitude drawn from P on the base meets the diagonal AD at point G. Find all possible vectors of G. It is given that the volume of the pyramid is 6sqrt3 cubic units and AP is 5 units.