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 and original cone volumes cannot be found from the information.
The original and replacement cones have the same volume.
The original cone holds more than the replacement.
To compare the volumes of the original and replacement cones, we can 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:
r = 1.5 inches, h = 4 inches
V = 1/3 * π * (1.5)^2 * 4
V = 3.14 * 2.25 * 4
V = 28.26 cubic inches
For the replacement cone:
r = 2 inches, h = 3 inches
V = 1/3 * π * (2)^2 * 3
V = 3.14 * 9 * 3
V = 28.26 cubic inches
Therefore, the original and replacement cones have the same volume. So, the correct response is: The original and replacement cones have the same volume.