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