A right circular cone has height 9 cms and radius of the base 5 cms.It is inverted
and water is poured into it.If at any instant the water level rises at the rate of `(pi/A)` cm/sec.
where A is the area of water surface at that instant,show that the vessel will be full in 75 seconds.

A cylinder of radius 12 cm contains water upto the height of 20 cm. A spherical iron ball is dropped into the cylinder and thus water level is raised by 6.75 cm. What is the radius of the ball ?

A cylindrical tank has a hole of 1cm^(2) in its bottom. If the water is allowed to flow into the tank from a tube above it at the rate of 70cm^(3)//sec , then the maximum height up to which water can rise in the tank is

A stone is dropped into a quiet lake and waves in the form of circles are generated, radius of the circular wave increases at the rate of 5cm/sec. At the instant when the radius of the circular wave is 8cm, how fast the area enclosed is increasing?

Water is being poured into a vessel in the form of an inverted right circular cone of semi vertical angle 45^@ in such a way that the rate of change of volume at any moment is proportional to the area of the curved surfaces which is wet at that moment.Initially the vessel is full to a height od 2 cm,after 2 seconds the height becomes 10 cm.Show that after 3.5 seconds from the start,the height of water will be 16 cm.

Water is being poured into a vessel in the form of an inverted right circular cone of semi vertical angle 45^@ in such a way that the rate of change of volume at any moment is proportional to the area of the curved surfaces which is wet at that moment.Initially the vessel is full to a height of 1 cm and after 1 second the height is 3 cm.Show that the height of the water after 3 seconds will be 7 cm.

If water is poured into an inverted hollow cone whose semi-vertical angle is 30^0 , so that its depth (measured along the axis) increases at the rate of 1 cm/sec. Find the rate at which the volume of water is increasing when the depth is 2 cm.