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 cone holds 2 times the amount as the replacement cone.
The original cone holds 2 times the amount as the replacement cone.
The original cone has a greater volume than the replacement cone.
The original cone has a greater volume than the replacement cone.
The original and replacement cones have the same volume.
The original and replacement cones have the same volume.
The replacement cone has a greater volume than the original cone.
The original cone has a greater volume than the replacement cone.
To calculate the volume of a cone, we 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 = 1/3 * π * 9 * 2 = 6π
For the replacement cone:
V = 1/3 * π * 1^2 * 6 = 1/3 * π * 1 * 6 = 2π
Therefore, the original cone holds 3 times the amount as the replacement cone.