Question

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

Answer 1

Given: a spherical ball salt, it is dissolving such that the rate of decrease of the volume at any instant is proportional to the surface

To prove: the radius is decreasing at a constant rate

Explanation: Let the radius of the spherical ball of the salt a t any time t be ‘r’.

Let the surface area of the spherical ball be S

Then, S = 4πr²……….(i)

Let V be the volume of the spherical ball,

Where k is the proportional constant

Substituting the values from equation (i) and (ii), we get

Hence the radius of the spherical ball is decreasing at a constant rate.

Hence Proved