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 and replacement cones have the same volume. The original and replacement cones have the same volume. 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 replacement cone holds more than the original.

Question

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 and replacement cones have the same volume. The original and replacement cones have the same volume. 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 replacement cone holds more than the original.

Answer 1

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.

For the original cone: r = 1.5 inches, h = 4 inches
V = (1/3)π(1.5)^2(4) = 9π cubic inches

For the replacement cone: r = 2 inches, h = 3 inches
V = (1/3)π(2)^2(3) = 4π cubic inches

Therefore, the volume of the original cone is 9π cubic inches, and the volume of the replacement cone is 4π cubic inches. The original cone holds more volume than the replacement cone.