Related Rates: sphere melting at 4cm^3/s; find change in r

[alliehatescalc]

I can't seem to figure out how to get this problem started..and I apologize if this is posted in the wrong format or something but this is my first post here so I don't know if I'm doing it right.. The problem:

A snowball in the shape of a sphere is melting in such a way that it is losing 4cm^3/sec. How fast is the radius of the snowball decreasing when the surface area of the snowball is 20pi cm^2? [Hint; note that v(t)= 4/3pi r^3(t) and surface area s(t)= 4pi r^2

any help would be greatly appreciated! thanks.

 

[stapel]

A snowball in the shape of a sphere is melting in such a way that it is losing 4cm^3/sec. How fast is the radius of the snowball decreasing when the surface area of the snowball is 20pi cm^2? [Hint; note that v(t)= 4/3pi r^3(t) and surface area s(t)= 4pi r^2.

You are given the formula for the surface area in terms of the radius, and you are given a value for the surface area at a particular time. Solve to find the radius at the time in question.

You are given the formula for the volume in terms of the radius, and you are given a value for the rate of change in the volume. Differentiate the formula implicitly with respect to time.

Plug in the given volume rate of change and the value you found for the radius. Solve for the required value.

If you get stuck, please reply with a clear listing of your work and reasoning so far. Thank you!

Eliz.

 

[alliehatescalc]

thank you so much- that was really helpful! =]