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 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 volume of a cone is calculated using the formula: V = (1/3) * π * r^2 * h, where r is the radius of the base and h is the height of the cone.
For the original cone with a diameter of 6 inches and a height of 2 inches:
r = 3 inches
h = 2 inches
V = (1/3) * π * (3)^2 * 2 = 12π cubic inches
For the replacement cone with a diameter of 2 inches and a height of 6 inches:
r = 1 inch
h = 6 inches
V = (1/3) * π * (1)^2 * 6 = 2π cubic inches
Therefore, the volume of the original cone is 12π cubic inches while the volume of the replacement cone is 2π cubic inches. Since 12π is 6 times greater than 2π, the original cone and the replacement cone have different volumes, not the same.