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.
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.
1 answer