Pete runs an ice cream stand that also sells snow cones served in paper cones.%C2%A0 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.%C2%A0 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 cone holds more than the replacement. The original cone holds more than the replacement. 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 and replacement cones have the same volume.
The original and replacement cones have the same volume.
Volume of original cone = (1/3) * pi * r^2 * h
Volume of replacement cone = (1/3) * pi * R^2 * H
Where r = 1.5 inches, h = 4 inches, R = 2 inches, and H = 3 inches
Substitute the values:
Volume of original cone = (1/3) * pi * (1.5)^2 * 4 = 9 pi
Volume of replacement cone = (1/3) * pi * (2)^2 * 3 = 8 pi
Therefore, the volumes of the original and replacement cones are not the same, and the original cone holds more volume than the replacement cone.