Pete runs an ice cream stand that also sells snow cones served in paper cones.
The paper cones he usually uses have a diameter of 3 inches and a height of 4 inches, but his supplier is out of them.
As a replacement, he purchases paper cones with a diameter of 4 inches and a height of 3 inches. How do the volumes of the original and replacement cones compare?
(2 points)
Responses
The replacement cone holds more than the original.
The replacement cone holds more than the original.
The original and replacement cones have the same volume.
The original and replacement cones have the same volume.
The replacement cone and original cone volumes cannot be found from the information.
The replacement cone and original cone volumes cannot be found from the information.
The original cone holds more than the replacement.
The original cone holds more than the replacement.
To compare the volumes of the cones, we can use the formula for the volume of a cone:
Original cone volume = (1/3)π(1.5^2)(4) ≈ 9.42 cubic inches
Replacement cone volume = (1/3)π(2^2)(3) = 8π cubic inches ≈ 25.13 cubic inches
Since the original cone holds approximately 9.42 cubic inches and the replacement cone holds approximately 25.13 cubic inches, we can conclude that the original cone holds more volume than the replacement cone.