A water tank has the shape of an inverted righ circular cone with its axis vertical and vertex lowermost . Its semi-vertical angle is `tan^(-1)(0.5)` . Water is poured into it at a constant rate of 4 cubic meter per hour . Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is 2 m.

A water tank has the shape of an inverted right circular cone with its axis vertical and vertex lowermost. Its semi-vertical angle is tan^(-1)(0.5) . Water is poured into it at a constant rate of 5 cubic meter per hour. Find the rate at which the level of the water is rising at the instant when the depth of water in the tank is 4 m.

Height of a tank in the form of an inverted cone is 10 m and radius of its circular base is 2 m. The tank contains water and it is leaking through a hole at its vertex at the rate of 0.02m^(3)//s. Find the rate at which the water level changes and the rate at which the radius of water surface changes when height of water level is 5 m.

A cylindrical tank has a hole of 1 cm in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of 70 cm//sec . then the maximum height up to which water can rise in the tank is

The capacity of a cuboidal tank is 50,000 litres of water. Find the breadth of the tank, if its length and depth are respectively 2.5 m and 10 m.

Water is pouring into a conical vessel of diameter 5.2m. And slant height 6.8 m(as shown in the adjoining ) , at the rate of 1.8 m^(3) per minute .How long will it take to fill the vessel?

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

A tank containing water has an orifice in one vertical side. If the centre of orifice is 4.9 m below the surface level in the tank, the velocity of discharge is:

A cylindrical tank of base area A has a small hole of areal a at the bottom. At time t=0 , a tap starts to supply water into the tank at a constant rate alpha m^(3)//s . (a) What is the maximum level of water h_(max) in the tank? (b) find the time when level of water becomes h(lt h_(max)) .

A thin equiconvex lens of glass of refractive index mu=3//2 & of focal length 0.3m in air is sealed into an opening at one end of a tank filled with water (mu=4//3) .On the opposite side of the lens ,a mirror is placed inside the tank on the tank wall perpendicular to the lens axis ,as shown in figure .the separation between the lens and the mirror is 0.8m A small object is placed outside the tank in front of the lens at a distance of 0.9 m form the lens along its axis .Find the position (relative to the lens)of the image of the object fromed by the stsyem.

A vessel is in the form of an inverted cone. Its height is 8 cm and radius of its top, which is open, is 5 cm. It is filled with water upto the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one fourth of the water flows out. Find the number of lead shots dropped in the vessel.