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)
To compare the volumes of the original and replacement cones, we can use the formula for the volume of a cone which is given by V = (1/3) * π * r^2 * h, where r is the radius of the base and h is the height.
For the original cone:
Radius (r) = 6 inches / 2 = 3 inches
Height (h) = 2 inches
Volume = (1/3) * π * 3^2 * 2 = (1/3) * π * 9 * 2 = 6π cubic inches
For the replacement cone:
Radius (r) = 2 inches / 2 = 1 inch
Height (h) = 6 inches
Volume = (1/3) * π * 1^2 * 6 = (1/3) * π * 1 * 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. The volume of the original cone is 3 times larger than the volume of the replacement cone.