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

Answer 1

To find the volume of a cone, you can use the formula V = 1/3 * π * r^2 * h, where r is the radius and h is the height.

Original cone:
Radius = 3/2 = 1.5 inches
Height = 4 inches
V = 1/3 * π * (1.5)^2 * 4 ≈ 9.42 cubic inches

Replacement cone:
Radius = 4/2 = 2 inches
Height = 3 inches
V = 1/3 * π * (2)^2 * 3 ≈ 12.57 cubic inches

Comparing the volumes, the replacement cone holds more ice cream/snow cone compared to the original cone.