Question

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?

A. The original cone has a greater volume than the replacement cone.
B. The original cone holds 2 times the amount as the replacement cone.
C. The replacement cone has a greater volume than the original cone.
D. The original and replacement cones have the same volume.

Answer 1

[AI-generated answer — Bot GPT 3.5]

B. The original cone holds 2 times the amount as the replacement cone.

To compare the volumes of the two cones, we can use the formula for the volume of a cone: V = 1/3 * π * r^2 * h, where r is the radius and h is the height of the cone.

For the original cone with a diameter of 6 inches, the radius is 3 inches 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 with a diameter of 2 inches, the radius is 1 inch and the height is 6 inches. So the volume of the replacement cone is V = 1/3 * π * 1^2 * 6 = 2π cubic inches.

Comparing the two volumes, the original cone holds 6π cubic inches while the replacement cone holds 2π cubic inches. Therefore, the original cone holds 3 times the amount as the replacement cone, and 3 is double the amount, so the correct answer is B.