"if a snowball melts so that its surface area decreases at a rate of 1 cm 2 min, find the rate at which the diameter decreases when the diameter is 10 cm." (stewart 249) stewart, james. single variable calculus, 8th edition. cengage learning, 20150101. vitalbook file.

We need to find the rate of the diameter, which we can denote as d(d)/dt.


, since it is decreasing.






At r = 5:




Since the diameter is twice the radius and this is simply the rate at which the radius is decreasing, then the diameter will be decreasing twice as fast:



Thus, the diameter is decreasing at a rate of 1/(20pi) cm/min.