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 288π ft3 288π ft3 216π ft3 216π ft3 48π ft3 48π ft3 36π ft3
The volume of a sphere is given by the formula V = 4/3 * π * r^3, where r is the radius of the sphere.
For the bottom snowball with a radius of 3 ft:
V1 = 4/3 * π * 3^3 = 4/3 * π * 27 = 36π ft^3
For the middle snowball with a radius of 2 ft:
V2 = 4/3 * π * 2^3 = 4/3 * π * 8 = 32π ft^3
For the top snowball with a radius of 1 ft:
V3 = 4/3 * π * 1^3 = 4/3 * π * 1 = 4π ft^3
The total volume of the snowman is the sum of the volumes of the three snowballs:
Total volume = V1 + V2 + V3
Total volume = 36π + 32π + 4π
Total volume = 72π ft^3
Therefore, the total volume of the snowman is 72π ft^3.