A spherical ball of salt is dissovlging water in such a manner that the rate of decrease of the volume at any instant is proportional to the surface. Prove that the radis is decreasing at a constant rate.

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

The surface area of spherical bubble is increasing at the rate of 2 [cm]^2/sec . Find the rate at which the volume of the bubble is increasing at the instant its radius is 6 cm.

The volume of a spherical balloon is increasing at the rate of 20 cm^3/sec . Find the rate at which its surface area is increasing at the instant when its radius is 4 cm.

The volume of a cube is increasing at a constant rate. Prove that the increase in its surface area varies inversely as the length of the side.

The radius of a cylinder is increasing at the rate of 2 cm/sec and the height is decreasing at the rate of 3 cm/sec. The rate of change of volume when the radius is 3 cm and height is 5 cm.

Spherical rain drop evaporates at a rate proportional to its surface area. The differential equation corresponding to the rate of change of the radius of the rain drop if the constant of proportionality is K gt 0 is

The radius of a cylinder is increasing at the rate of 2m/s. and its altitude is decreasing at the rate of 3m/s. Find the rate of change of volume when radius is 3 metres and altitude is 5 metres.

Water is leaking from a conical funnel at a uniform rate of 4 cm^3//sec thorugh at small hole at the vertex. When the slant height of the water in the funnel is 3 cm, find the rate of decrease of the slant height of water given that semi vertical angle of the cone (funnel) is 30^@ .

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

A spherical balloon is filled with 4500pi cubic metres of helium gas. If a leak in the balloon causes the gas to escape at the rate of 72pi cubic metres per minute, then the rate (in metres per minute) at which the radius of the balloon decreases 49 minutes after the leakage begins is :