Frosty Is Melting!

Age 14 to 16
Challenge Level

The volume of a sphere is given by $V=\frac 4 3 \pi  r^3$

Can you use this to find the initial volume of Frosty in terms of $R?$
Remember that Frosty is made of two snowballs!

What is the initial height of Frosty?
What is the height of Frosty when it is half its height?

Given that the radius of each snowball decreases by the same amount each minute, can you find the radii of each sphere when Frosty is half his height?

You can now find the new volume of Frosty in terms of $R$.

The last part of the question, "What is this ratio when Frosty is one-tenth of his initial height?" looks very similar to the first part, but there is a crucial difference!  To answer this part, think about what happens to a snowman as it melts.