A sheet of area `40m^2` is used to make an open tank with square base. Find the dimensions of the base such that the volume of this tank is maximum.

An open tank of volume 32 cu. Metre consists of a square base with vertical sides. Find the dimensions of the tank when the expense of lining it with lead is minimum.

An open box with a square base is made out of a given iron sheet of area 27 sq.m. Then, the maximum volume of the box is-

The volume of an open tank with a square base of side x m is 40m^3 . Express its total surface area as a function of x.

A regular square pyramid is 3m Height and the perimeter of its base is 16 m. Find the volume of the pyramid.

The volume of a right circualr cylinder varies as the square of the radius of its base , when its height is constant and as the height when the radius of the base is constant . The volume of a cylinder the radius of whose base and height are respectively 2 metres and 7 metres is 88 cubic metres . The volume and radius of the base of a cylinder are 396 cubic metres and 9 metres respectively . Detemine the height of the cylinder.

The base of a water tank is a square of side 3 ft. find the rate of flow of water in the tank, if the water-level at the rate of 1 fr/min.

A box, constructed from a rectangular metal sheet, is 21 cm by 16cm by cutting equal squares of sides x from the corners of the sheet and then turning up the projected portions. The value of x so that volume of the box is maximum is (a) 1 (b) 2 (c) 3 (d) 4

Find the volume of a pyramid whose square base is 10 cm. and height 8 cm.

If the area of the base of a right circular cone be 4pi r^2 sq-cm and height be 3 cm , then the volume of the cone will be