To find the total volume of the snowman made of three spherical snowballs, we can use the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
We will calculate the volume for each snowball and then sum them up.
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Volume of the bottom snowball (radius = 3 ft): \[ V_1 = \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi (27) = 36\pi \text{ ft}^3 \]
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Volume of the middle snowball (radius = 2 ft): \[ V_2 = \frac{4}{3} \pi (2)^3 = \frac{4}{3} \pi (8) = \frac{32}{3} \pi \text{ ft}^3 \]
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Volume of the top snowball (radius = 1 ft): \[ V_3 = \frac{4}{3} \pi (1)^3 = \frac{4}{3} \pi (1) = \frac{4}{3} \pi \text{ ft}^3 \]
Now, we can sum the volumes of the three snowballs: \[ V_{total} = V_1 + V_2 + V_3 = 36\pi + \frac{32}{3}\pi + \frac{4}{3}\pi \]
First, we will convert \(36\pi\) to a fraction with a denominator of 3: \[ V_1 = 36\pi = \frac{108}{3}\pi \]
Now we can sum the volumes with a common denominator: \[ V_{total} = \frac{108}{3} \pi + \frac{32}{3} \pi + \frac{4}{3} \pi \] \[ V_{total} = \frac{108 + 32 + 4}{3}\pi = \frac{144}{3}\pi = 48\pi \text{ ft}^3 \]
Thus, the total volume of the snowman is \[ \boxed{48\pi \text{ ft}^3} \]