Question

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?

Answer 1

wrong

Answer 2

To find the volume of each snowball, we can use the formula for the volume of a sphere:

V = (4/3) * π * r^3

For the bottom snowball with a radius of 3 ft:
V1 = (4/3) * π * (3)^3
V1 = (4/3) * π * 27
V1 = 36π

For the middle snowball with a radius of 2 ft:
V2 = (4/3) * π * (2)^3
V2 = (4/3) * π * 8
V2 = 32π

For the top snowball with a radius of 1 ft:
V3 = (4/3) * π * (1)^3
V3 = (4/3) * π * 1
V3 = 4π

To find the total volume of the snowman, we simply add the volumes of each snowball together:

Total volume = V1 + V2 + V3
Total volume = 36π + 32π + 4π
Total volume = 72π

Therefore, the total volume of the snowman is 72π cubic feet.

Answer 3

Apologies for the mistake. Let's calculate the correct total volume of the snowman.

The volume of a sphere is given by the formula:

V = (4/3) * π * r^3

For the bottom snowball with a radius of 3 ft:
V1 = (4/3) * π * (3)^3
V1 = (4/3) * π * 27
V1 = 36π

For the middle snowball with a radius of 2 ft:
V2 = (4/3) * π * (2)^3
V2 = (4/3) * π * 8
V2 = 32π

For the top snowball with a radius of 1 ft:
V3 = (4/3) * π * (1)^3
V3 = (4/3) * π * 1
V3 = 4π

Now, to find the total volume of the snowman, we add the volumes of the individual snowballs:

Total volume = V1 + V2 + V3
Total volume = 36π + 32π + 4π
Total volume = 72π

Therefore, the correct total volume of the snowman is 72π cubic feet.