We may first write all of the information given in mathematical notation:

In order that the problem have an answer, the ratio of the height to the radius, and thus the angle of the tip of the cone, must remain the same. (Otherwise, we could have the cone start out narrow and then get wider as approaches , lowering our answer for dramatically.) Therefore, we may say that

for some , and that

In order to find the value of at , in minutes, we may use the equations above together with the fact that