An open tank of a given capacity has square base with vertical sides . Prove that the expense of lining the the tank with cement will be minimum if the height of the tank is half the width.

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.

A cylindrical tin can open at the top , of a given capacity has to be constructed . Show that the amount of the tin required will be least if the height of the can is equal to its radius

A cylindrical tin can, open at the top, of a given capacity has to be constructed, show that the amount of the tin required will be least if the height of the can is equal to its radius.

Using vectors , prove that the line joining the midpoints of two sides of a triangle, is parallel to the base and half its length.

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.

Answer any two questions : If 64 buckets of water is withdrawn from a cubical water tank, full of water, then 1/3 of water in the tank still remains. If the length of the side of the water tank is 1.2 metre than what is the capacity (in litre) of each bucket? (1 cubic decimeter = 1 litre)

Water is drained from a vertical cylindrical tank by opening a value at the base of the tank. It is known that the rate at which the water level drops is proportional to the square root of water depth y, where the constant of proprortionality kgt0 depends on the acceliration due to gravity and the geomety of the hole. If is measured in minutes and k=(1)/(15) then the time of drain the tank, If the water is 4 m deep to start with is

A TV tower stands vertically on the side of a road. From a point on the other side directly opposite to the tower, the angle of elevation of the top of tower is 60^(@) From another point 1m away from this point, on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is 30^(@) . Find the height of the tower and the width ofthe road.

An overhead water tanker is in the shape of a cylinder has capacity of 61.6 cu.mts. The diameter of the tank is 5.6 m. Find the height of the tank.

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.