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 original cone holds more than the replacement.
The original cone holds more than the replacement.
The replacement cone holds more than the original.
The replacement cone holds more than the original.
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 a cone = (1/3) * π * r^2 * h
For the original cone:
r = 1.5 inches, h = 4 inches
Volume = (1/3) * π * (1.5)^2 * 4 = 9π cubic inches
For the replacement cone:
r = 2 inches, h = 3 inches
Volume = (1/3) * π * (2)^2 * 3 = 8π cubic inches
Since 9π = 9 * 3.14 and 8π = 8 * 3.14, the volumes of the original and replacement cones are equal.