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 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.
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 and replacement cones have the same volume.
The original cone has a greater volume than the replacement cone.
To compare the volumes of the cones, we use the formula for the volume of a cone: V = 1/3 * π * r^2 * h, where r is the radius and h is the height.
For the original cone with a diameter of 6 inches and a height of 2 inches:
- Radius = 6/2 = 3 inches
- Volume = 1/3 * π * 3^2 * 2 = 6π cubic inches
For the replacement cone with a diameter of 2 inches and a height of 6 inches:
- Radius = 2/2 = 1 inch
- Volume = 1/3 * π * 1^2 * 6 = 2π cubic inches
The original cone holds 3 times the amount as the replacement cone.