Problem

Suppose the snowball in Problem 21 melts so that the rate of change in its diameter is proportional to its surface area. Using the same given data, determine when its diameter will be 2 in. Mathematically speaking, when will the snowball disappear?

In this question using the data of question 21 of the textbook we have to determine when the

diameter of snowball be 2m and when will the snowball will finally disappear.

Step 1</p>

Let D be the diameter of snowball

Volume =

Surface area =

=

also it is given that

Change in diameter ∝ Surface area

-ve sign indicates that snowball is melting.

Step 2 </p>

Integrating both sides with limit