A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to 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.

An inverted conical vessel whose height is 10 cm and the radisu of whse base is 5 cm is being filled with water at the uniform rate of 1.5 cu cm/m. Find the rate at which the level of water in the vessel is rising when the depth is 4 cm.

A cone of radius 4 cm is filled with water. If the water is poured in a cylinder of radius 8 cm, the height of the water rises 2 cm, find the heiht of the cone.

From a top of inner radius 0.75 cm, water flows at the rate of 7 m per second. Find the volume in litres of water delivered by the pipe in one hours.

A mass of 10 kg is dropped form a height of 50 cm. Find its velocity with which it hits the ground.

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 metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. Find how many cones are obtained ?

The radius of a spherical soap bubble is increasing at the rate of 0.5 cm per second. Find the rate of change of its volume, when the radius is 10 cm.

The radius of a soap-bubble is increasing at the rate of 0.2cm/s. Find the rate of increase of its volume when the radius is 5 cm.

A container, opened from the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8cm and 20 cm, respectively. Find the cost of the milk which can completely fill the container, at the rate of ₹ 20 per litre. Also find the cost of metal sheet used to make the container, if it costs ₹8 per 100 cm^2 ( Take pi = 3. 14 )