Physics in maths

Calculus Level 4

A spherical water droplet evaporates at a rate proportional to its surface area at any instant t. The rate of change of the radius of the water drop is:

proportional to surface area proportional to volume none of these proportional to radius proportional to square of surface area

1 solution

Théo Leblanc
Jun 16, 2019

Let $V$ the volume of the droplet. We are given that: $\dfrac{dV}{dt} \propto S \propto R^2$

Because $V \propto R^3, \quad \dfrac{dV}{dt} \propto \dfrac{dR}{dt}\times R^2$

Thus $\dfrac{dR}{dt} \propto 1$

ie $\boxed{\dfrac{dR}{dt}=cst}$

Physics in maths

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