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. Prove that the radius is decreasing at a constant rate.

Explanation

Given,

`((dV)/dt)​=Kxx`(surface area)

we know,

`V=4/3​pir^3`

`S=4pir^2`

`(((d4)/3​pir^3)/dt)​=Kxx(4pir^2)`

=`(4pi)/3 ​(dr^3)/dt​=4piKr^2`

=`(4pi)/3xx 3r^2 xx((dr)/dt)​=4piKr^2`

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