Susie runs an ice cream stand that also sells snow cones served in paper cones. The paper cones she usually uses have a diameter of 6 inches and a height of 2 inches, but her supplier is out of them. As a replacement, she purchases paper cones with a diameter of 2 inches and a height of 6 inches. How do the volumes of the original and replacement cones compare? (1 point) Responses The original cone holds 2 times the amount as the replacement cone. The original cone holds 2 times the amount as the replacement cone. The replacement cone has a greater volume than the original cone. The replacement cone has a greater volume than the original cone. The original and replacement cones have the same volume. The original and replacement cones have the same volume. The original cone has a greater volume than the replacement cone. The original cone has a greater volume than the replacement cone.
The original cone has a greater volume than the replacement cone.
To calculate the volume of a cone, you can use the formula V = 1/3 * π * r^2 * h, where r is the radius of the base and h is the height of the cone.
For the original cone:
r = 3 inches (diameter of 6 inches / 2)
h = 2 inches
V(original) = 1/3 * π * 3^2 * 2 = 18π cubic inches
For the replacement cone:
r = 1 inch (diameter of 2 inches / 2)
h = 6 inches
V(replacement) = 1/3 * π * 1^2 * 6 = 2π cubic inches
Therefore, the original cone has a greater volume than the replacement cone as 18π > 2π.