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?
To find the volume of each snowball, we use the formula for the volume of a sphere: V = (4/3)πr^3
For the bottom snowball:
V1 = (4/3)π(3^3) = (4/3)π(27) = 36π ft^3
For the middle snowball:
V2 = (4/3)π(2^3) = (4/3)π(8) = 32π ft^3
For the top snowball:
V3 = (4/3)π(1^3) = (4/3)π(1) = 4π ft^3
Now, adding up the volumes of each snowball, we get:
Total Volume = V1 + V2 + V3
Total Volume = 36π + 32π + 4π
Total Volume = 72π ft^3
Therefore, the total volume of the snowman is 72π cubic feet.