An open tank is to be constructed with square base and vertical sides so as to contain a given quantity of water. Show that the expenses of lining with lead will be least, if depth is made half of width.

An open tank with a square base and vertical sides is to be constructed form a metal sheet so as to hold a given quantity of water. Show that the cost of material will be least when depth of tank is half its width. If the cost is to be borne by nearby settled lower income families, for whom water will be provided, what kind of value is hidden in the question

A metal box with a square base and vertical sides is to contain 1024 cm3 of water, the material for the top and bottom costs Rs 5 per cm2 and the material for the sides costs Rs 2.50 per cm2. Find the least cost of the box.

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

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

OR An open box with a square base is to be made out of a given quantity of cardboard of area \ c^2 square units. Show that the maximum volume of the box is (c^3)/(6\ sqrt(3)) cubic units.

A liquid having density 6000 kg//m^(3) stands to a height of 4 m in a sealed tank as shown in the figure. The tank contains compressed air at a gauge pressure of 3 atm . The horizontal outlet pipe has a cross-sectional area of 6 cm^(2) and 3 cm^(2) at larger and smaller sections. Atmospheric pressure = 1 atm, g = 10m//s^(2) 1 atm =10^(5) N//m^(2) . Assume that depth of water in the tank remains constant due to s very large base and air pressure above it remains constant. Based on the above information, answer the following questions. The height at which liquid will stand in the open end of the pipe is

A tank with rectangular base and rectangular sides open at the top is to be constructed so that its depth is 3 m and volume is 75 m3. If building of tank costs Rs. 100 per square metre for the base and Rs. 50 per square metres for the sides, find the cost of least expensive tank.

A tank with rectangular base and rectangular sides open at the top is to be constructed so that its depth is 3 m and volume is 75 "m"^3 . If building of tank costs Rs. 100 per square metre for the base and Rs. 50 per square metre for the sides, find the cost of least expensive tank.

A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2m and volume is 8 m^3 . If building of tank costs Rs. 70 per sq. metre for the base and Rs. 45 per sq. metre for sides, what is the cost of least expensive tank?

Water is drained from a vertical cylindrical tank by opening a valve 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 proportionality k >0 depends on the acceleration due to gravity and the geometry of the hole. If t is measured in minutes and k=1/(15), then the time to drain the tank if the water is 4 m deep to start with is (a) 30 min (b) 45 min (c) 60 min (d) 80 min