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)
The replacement cone has a greater volume than the original cone.
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.
The original cone and the replacement cone have the same volume.
To calculate the volume of a cone, you use the formula V = (1/3) * π * r^2 * h, where r is the radius of the base of the cone and h is the height of the cone.
For the original cone: r = 6/2 = 3 inches, h = 2 inches.
V_original = (1/3) * π * (3)^2 * 2 = 6π cubic inches.
For the replacement cone: r = 2/2 = 1 inch, h = 6 inches.
V_replacement = (1/3) * π * (1)^2 * 6 = 2π cubic inches.
Therefore, the volume of the original cone is 6π cubic inches and the volume of the replacement cone is 2π cubic inches. Since 6π is three times larger than 2π, the original cone has a greater volume than the replacement cone.