A fish in tank sees the outside world as if it is at the vertex of a cone such that the circular base of the cone is at the surface of the water.If the depth of the fish is d and the critical angle for water-air interface is C,what is the radius of circle?

For glass-air interface,the critical angle is C.Will the critical angle for glass-water interface be greater or less than C?

A fish looking up through the water sees the outside world contained in a circular horizon.If the refractive index of water is 4//3 and fish is 12 cm below the surface of water,then the radius of the circular horizon is

A luminous object is paced just below a glass slab of thickness t. A circular opaque disc is placed vertically above on the surface of the glass-slab. If C is critical angle for glass-air interface, then predict the minimum radius of the opaque disc so that the object cannot be seen from any uncovered portion of the glass-slab.

A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is tan ^(-1)((1)/(2)) . Water is poured into it at a constant rate of 5 cu m/min. Then, the rate (in m/min) at which the level of water is rising at the instant when the depth of water in the tank is 10 m. Water is a natural resource. What is the importance of water in our daily life?

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.

Water is dripping out from a conical funnel at a uniform rate of 4c m^3//sec through a tiny hole at the vertex in the bottom. When the slant height of the water is 3cm , find the rate of decrease of the slant height of the water-cone. Given that the vertical angle of the funnel is 120^0dot

An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of the same metallic sheet (see Fig. 13.23). The diameters of die two circular ends of the bucket are 45 cm and 25 cm, the total vertical height of the bucket is 40 cm and that of the cylindrical base is 6 cm. Find the area of the metallic sheet used to make the bucket, where we do not take into account the handle of the bucket. Also, Find the volume of water the bucket can hold. (Take pi=22/7 ).

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 m^3/h . 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 .

A right circular cone of diameter r cm and height 12 cm rests on the base of a right circular cylinder of radius r cm. Their bases are in the same plane and the cylinder is filled with water upto a height of 12 cm. If the cone is removed, find the height to which water level fall.