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?
The Origin of the Snowman (2020) – Kern Valley Highlights
a
\large 288\pi ft^3
b
\large 48\pi ft^3
c
\large 216\pi ft^3
d
\large 36\pi ft^3
To find the total volume of the snowman, we need to find the volume of each snowball and then add them together.
Volume of the bottom snowball:
V1 = (4/3) * π * (3^3)
V1 = (4/3) * π * 27
V1 = 36π ft^3
Volume of the middle snowball:
V2 = (4/3) * π * (2^3)
V2 = (4/3) * π * 8
V2 = 32π/ 3 ft^3
Volume of the top snowball:
V3 = (4/3) * π * (1^3)
V3 = (4/3) * π * 1
V3 = 4π/3 ft^3
Total volume of the snowman:
V_total = V1 + V2 + V3
V_total = 36π + 32π/3 + 4π/3
V_total = 72π/3 + 32π/3 + 4π/3
V_total = 108π/3
V_total = 36π ft^3
Therefore, the total volume of the snowman is 36π ft^3.
Therefore, the correct option is:
d) 36π ft^3
Are you 100% sure
Let's double-check the calculations:
Volume of the bottom snowball:
V1 = (4/3) * π * (3^3) = (4/3) * π * 27 = 36π ft^3
Volume of the middle snowball:
V2 = (4/3) * π * (2^3) = (4/3) * π * 8 = 32π ft^3
Volume of the top snowball:
V3 = (4/3) * π * (1^3) = (4/3) * π * 1 = 4π/3 ft^3
Total volume of the snowman:
V_total = V1 + V2 + V3 = 36π + 32π + 4π/3 = 72π + 4π/3 = 216π/3 = 72π ft^3
Therefore, the correct total volume of the snowman is 72π ft^3.
The correct option is:
c) \(216π ft^3\)
Are you sure
I apologize for the mistake in my previous response. Let's go through the calculations one more time to ensure accuracy.
Volume of the bottom snowball:
V1 = (4/3) * π * (3^3) = (4/3) * π * 27 = 36π ft^3
Volume of the middle snowball:
V2 = (4/3) * π * (2^3) = (4/3) * π * 8 = 32π/3 ft^3
Volume of the top snowball:
V3 = (4/3) * π * (1^3) = (4/3) * π * 1 = 4π/3 ft^3
Total volume of the snowman:
V_total = V1 + V2 + V3 = 36π + 32π/3 + 4π/3 = 108π/3 = 36π ft^3
Therefore, the total volume of the snowman is indeed 36π ft^3.
The correct option is:
d) \(36π ft^3\)
Bro please just choose the correct answerrrr
I apologize for the confusion in my previous responses. The correct total volume of the snowman is:
d) \(36π ft^3\)