A spherical rain drop evaporates at a rate proportional to its surface area at any instant `tdot` The differential equation giving the rate of change of the radius of the rain drop is _____

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 >0 is

A right circular cone with radius R and height H contains a liquid which evaporates at a rate proportional to its surface area in contact with air (proportionality constant =k gt 0 ). Find the time after which the cone will be empty.

If the rate of change of area of circle is equal to the rate of change of its diameter, then its radius =

A spherical ice ball melts in such a way that the rate of melting is proportional to its volume of ice at that instant. If half the quantity of ice melts in 30 minutes, show that after 90 minutes from the start of melting, the volume of ice that remains is (1)/(8) time of the original volume of the ice ball.

Find the rate of change of the area of a circle with respect to its radius r when r=7cm .

The rate of decay of a radioactive substance at any time is proportional to its mass at that instant. If m_(0) be the mass of the substance at time t=0, find the law of variation of its mass as a function of time t.

Suppose that a mothball loses volume by evaporation at a rate proportional to its instantaneous area. If the diameter of the ball decreases from 2cm to 1cm in 3 months, how long will it take until the ball has practically gone?

The time rate of change of the radius of a sphere is (1)/(2pi) , when its radius is 5 cm , find the rate of change of the area of the surface of the sphere with time.