Question

A spherical snowball melts at a rate proportional to its surface area. (a) write a differential equation for its volume, v. (use k for the constant of proportionality.) dv dt = correct: your answer is correct. (b) if the initial volume is s, solve the differential equation.

Answer 1

Answer:

Explanation:

The rate of change in volume is proportional to the surface area:

dV/dt = kA

Integrating:

V = kAt + C

At t=0, V = s, so:

s = kA(0) + C

C = s

Therefore:

V = kAt + s