Carlos has built a snowman consisting solely of 3 spherical snowballs.

First, we need to find the volume of each snowball using the formula for the volume of a sphere: V = (4/3)πr^3.

For the bottom snowball: V = (4/3)π(3)^3 = 36π ft^3
For the middle snowball: V = (4/3)π(2)^3 = 32π ft^3
For the top snowball: V = (4/3)π(1)^3 = 4π ft^3

Now, to find the total volume of the snowman, we add the volumes of each snowball together: 36π + 32π + 4π = 72π + 32π + 4π = 108π ft^3

Therefore, the total volume of the snowman is 108π ft^3.

The closest answer choice is 108π ft^3.