Susie runs an ice cream stand that also sells snow cones served in paper cones.
The paper cones she usually uses have a diameter of 6 inches and a height of 2 inches, but her supplier is out of them.
As a replacement, she purchases paper cones with a diameter of 2 inches and a height of 6 inches. How do the volumes of the original and replacement cones compare?
(1 point)
Responses
The original and replacement cones have the same volume.
The original and replacement cones have the same volume.
The original cone holds 2 times the amount as the replacement cone.
The original cone holds 2 times the amount as the replacement cone.
The replacement cone has a greater volume than the original cone.
The replacement cone has a greater volume than the original cone.
The original cone has a greater volume than the replacement cone.
The original cone has a greater volume than the replacement cone.
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The original cone has a greater volume than the replacement cone.
To calculate the volume of a cone, you use the formula V = 1/3 * π * r^2 * h, where r is the radius and h is the height.
For the original cone:
V = 1/3 * π * (3)^2 * 2 = 12π cubic inches
For the replacement cone:
V = 1/3 * π * (1)^2 * 6 = 2π cubic inches
Since 12π > 2π, the original cone has a greater volume than the replacement cone.