The rate (in cubic feet per hour) that a spherical snowball melts is proportional to the snowball's volume raised to the 2/3 power. (This assumes that the rate snow melts is proportional to the area exposed to the air - - i. e. the surface area of the snowball.) If a snowball of radius 1 foot (volume 4/3 / [Pi] cubic feet) melts in 6 hours, how long will it take a snowball of raduis 3 feet (volume 36 cubic feet) to melt?

A 3 feet radius snowball will melt in 54 hours.

Explanation:

As we can assume that the rate of snowball takes to melt is proportional to the surface area, then the rate for a 3 feet radius will be:

T = A (3 ft) / A (1 ft) * 6 hr

A is the area of the snowballs. For a spherical geometry is computing as:

A=4. pi. R^2

Then dividing the areas:

A (3 feet) / A (1 foot) = (4 pi (3 ft) ^2) / (4 pi (1 ft) ^2) = (36pi ft^2) / (4pi ft^2) = 9

Finally, the rate for the 3 feet radius snowball is:

T = 9 * 6 hr = 54 hr