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 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 replacement cone has a greater volume than the original cone.
The original cone has a greater volume than the replacement cone.
To compare the volumes of the cones, we can use the formula for the volume of a cone: V = (1/3)πr^2h, where r is the radius and h is the height of the cone.
For the original cone:
r = 3 inches (radius is half of the diameter)
h = 2 inches
V = (1/3)π(3)^2(2) = 6π cubic inches
For the replacement cone:
r = 1 inch (radius is half of the diameter)
h = 6 inches
V = (1/3)π(1)^2(6) = 2π cubic inches
Comparing the volumes:
Original cone = 6π cubic inches
Replacement cone = 2π cubic inches
Since 6π is greater than 2π, the original cone has a greater volume than the replacement cone.