The original cone has a volume of (1/3)π(1.5^2)4 = 9π cubic inches.
The replacement cone has a volume of (1/3)π(2^2)3 = 4π cubic inches.
Therefore, the original cone holds more than the replacement.
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)
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.
3 answers
are u sure
Apologies for the mistake in my previous response. Let's calculate the correct volumes of the cones:
Original cone:
Volume = (1/3) * π * radius^2 * height
Volume = (1/3) * π * (1.5)^2 * 4
Volume = 3 * π
Replacement cone:
Volume = (1/3) * π * radius^2 * height
Volume = (1/3) * π * (2)^2 * 3
Volume = 4 * π
Therefore, the replacement cone holds more ice cream than the original cone.
The replacement cone holds more than the original.
Original cone:
Volume = (1/3) * π * radius^2 * height
Volume = (1/3) * π * (1.5)^2 * 4
Volume = 3 * π
Replacement cone:
Volume = (1/3) * π * radius^2 * height
Volume = (1/3) * π * (2)^2 * 3
Volume = 4 * π
Therefore, the replacement cone holds more ice cream than the original cone.
The replacement cone holds more than the original.