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. The radius is decreasing at a constant rate.

• A. True
• B. False

Answer 1

The correct option is A True

According to the question

$\frac{dV}{dt}=K\times$(surface area)

$V=\frac{4}{3}\pi r^3,SA=4\pi r^2$

$\frac{d\left(\frac{4}{3}\pi r^3\right)}{dt}=K\times 4\pi r^2$

$\frac{4\pi }{3}\frac{d{r}^3}{dt}=4\pi K{r}^2$

$\frac{4\pi }{3}\times 3r^2\times \frac{dr}{dt}=4\pi K{r}^2$

$\frac{dr}{dt}=K$

Hence true.