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

We have, rate of decrease of the volume of spherical ball of salt at any instant is `propto` surface.
Let the radius of the spherical ball of the salt be r.
`therefore` Volume of the ball (V) `=4/3pir^(3)`
and surface area (S) = `4pir^(2)`
`therefore (dV)/(dt) propto S rArr d/(dt) (4/3pir^(3)) propto 4pir^(2)`
`rArr 4/3.pi.3r^(2).(dr)/(dt) propto 4pir^(2) rArr (dr)/(dt) propto (4pir^(2))/(4pir^(2))`
`(dr)/(dt) = k.1` [where, k is the proportionally constant]
`rArr (dr)/(dt) = k`
Hence, the radius of ball is decreasing at a constant rate.