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)
O The replacement cone and original cone volumes cannot be found from the information.
The replacement cone holds more than the original.
O The original cone holds more than the replacement.
The original and replacement cones have the same volume.
The volume of a cone is calculated using the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
For the original cone with a diameter of 3 inches, the radius is 1.5 inches and the height is 4 inches. So, the volume of the original cone is V = (1/3) * π * (1.5)^2 * 4 = 9π cubic inches.
For the replacement cone with a diameter of 4 inches, the radius is 2 inches and the height is 3 inches. So, the volume of the replacement cone is V = (1/3) * π * (2)^2 * 3 = 4π cubic inches.
Comparing the volumes, we see that 9π > 4π, so the original cone holds more ice cream than the replacement cone.
Therefore, the original cone holds more than the replacement.