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

Ball of salt is spherical


`therefore` Volume of ball, `{V}=frac{4}{3} pi {r}^{3}`


Where `r=` radius of the ball


As per the question, `frac{d V}{d t} infty S`


Where `S=` surface area of the ball



`Rightarrow frac{d}{d t}(frac{4}{3} pi r^{3}) infty 4 pi r^{2} quad ldots ldots[ {S}=4 pi r^{2}] `


`Rightarrow frac{4}{3} pi cdot 3 r^{2} cdot frac{d r}{d t} infty 4 pi r^{2} `


...