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?

Question

A. 216π
B. 48π
C. 288π
D. 36π

Answer 1

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.