Carlos has built a snowman consisting solely of 3 spherical snowballs. The bottom snowball has a radius of 3 ft, the middle snowball has a radius of 2 ft, and the top snowball has a radius of 1 ft. What is the total volume of the snowman?
The Origin of the Snowman (2020) – Kern Valley Highlights
a
\large 48\pi ft^3
b
\large 216\pi ft^3
c
\large 36\pi ft^3
d
\large 288\pi ft^3
c
36\pi ft^3
c
36\pi ft^3c
36\pi ft^3c
36\pi fteterhrwth3y6rtyjtmvtrh0eygm00gyowtnvnygebgrc
error gate 404
huh
To find the total volume of the snowman, we need to calculate the volume of each snowball separately and then add them together.
To calculate the volume of a sphere, we use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where V is the volume and r is the radius.
For the bottom snowball, the radius is 3 ft.
\[ V_1 = \frac{4}{3} \pi (3^3) = \frac{4}{3} \pi 27 = 36 \pi ft^3 \]
For the middle snowball, the radius is 2 ft.
\[ V_2 = \frac{4}{3} \pi (2^3) = \frac{4}{3} \pi 8 = \frac{32}{3} \pi ft^3 \]
For the top snowball, the radius is 1 ft.
\[ V_3 = \frac{4}{3} \pi (1^3) = \frac{4}{3} \pi 1 = \frac{4}{3} \pi ft^3 \]
Now, we can add up the volumes of each snowball to find the total volume of the snowman:
\[ V_{total} = V_1 + V_2 + V_3 = 36 \pi + \frac{32}{3} \pi + \frac{4}{3} \pi = \frac{108}{3} \pi + \frac{32}{3} \pi + \frac{4}{3} \pi = \frac{144}{3} \pi = 48 \pi ft^3 \]
Therefore, the total volume of the snowman is \(\boxed{\textbf{(a) } 48\pi ft^3}\).