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?
(1 point)
Responses
48π ft3
48π ft3
288π ft3
288π ft3
36π ft3
36π ft3
216π ft3
288π ft3
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 = 36π ft3
For the middle snowball: V2 = (4/3)π(2)^3 = 32π ft3
For the top snowball: V3 = (4/3)π(1)^3 = 4π ft3
The total volume of the snowman is the sum of these three volumes: V_total = 36π + 32π + 4π = 72π + 4π = 76π
Therefore, the total volume of the snowman is 76π ft3.