Susie runs an ice cream stand that also sells snow cones served in paper cones.%C2%A0 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.%C2%A0 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 replacement cone has a greater volume than the original cone. The replacement cone has a greater volume than the original cone. The original cone has a greater volume than the replacement cone. The original cone has a greater volume than the replacement cone. The original and replacement cones have the same volume. The original and replacement cones have the same volume. The original cone holds 2 times the amount as the replacement cone.
The original cone has a greater volume than the replacement cone.
To calculate the volume of a cone, you use the formula V = (1/3) * π * r^2 * h, where r is the radius and h is the height.
For the original cone, the radius is 3 inches (half of the diameter) and the height is 2 inches. So, the volume of the original cone is V = (1/3) * π * 3^2 * 2 = 6π cubic inches.
For the replacement cone, the radius is 1 inch (half of the diameter) and the height is 6 inches. So, the volume of the replacement cone is V = (1/3) * π * 1^2 * 6 = 2π cubic inches.
Since 6π > 2π, the original cone has a greater volume than the replacement cone.