A spherical snowball melts at a rate proportional to its surface area. Show that the rate of change of the radius is constant.(adsbygoogle = window.adsbygoogle || []).push({});

Two ratios are proportional if they change equally and are related by a constant of proportionality? Not sure about this definition, but please correct it if you can.

My initial thoughts were to set up an equation and differentiate it with respect to time.

S=surface area, r=radius, k=constant of proportionality

S=4pir^2=s

(dS/dt)=2*4*pi*r*(dr/dt)

(dr/dt)=[(dS/dt)]/[(8pir)]

At this point, I do not know what to do.

The words I am using to describe the situation: The rate at which the snowball melts (dS/dt) is proportional to the radius. So the radius is the constant of proportionality? I am thinking that we should have something like the following: (d/s/dt)=constant of proportionality*surface area?

I am not sure how to understand this problem.

Please explain the problem. There is nothing worse than a teacher that does a bunch of math on a chalkboard, gives the most minute explanation, and calls it teaching (just my opinion)

Please use words and explain what is happening. Thanks

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