Calculus question

Question

While you were out cross country skiing, you make a perfectly shaped spherical snowball. Unfortunately the temperature increases and the volume of your snowball decreases at a rate of -1cm/min. At what rate is the radius decreasing when the radius is 5cm? 

Help!?

Answer 1

This is a related rates question using implicit differentiation.  

 

V = (4/3)*pi*r³

 

Taking the derivative with respect to time, you get:

(dV/dt) = 4*pi*r²*(dr/dt)

-1 = 4*pi*25*(dr/dt)

-1 = 100*pi*(dr/dt)

(dr/dt) = -1/(100*pi) cm/min