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. What is the total volume of the snowman?
A. 216π
B. 48π
C. 288π
D. 36π
To find the volume of each snowball, we can use the formula for the volume of a sphere: V = 4/3πr^3, where r is the radius.
For the bottom snowball:
V1 = 4/3π(3)^3
V1 = 4/3π(27)
V1 = 36π
For the middle snowball:
V2 = 4/3π(2)^3
V2 = 4/3π(8)
V2 = 32π
For the top snowball:
V3 = 4/3π(1)^3
V3 = 4/3π(1)
V3 = 4π
Now, to find the total volume of the snowman, we add the volumes of each snowball:
Total volume = V1 + V2 + V3
Total volume = 36π + 32π + 4π
Total volume = 72π
Therefore, the total volume of the snowman is 72π, which is closest to option C. 288π.