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?

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.

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1 answer
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Answer 1

Bot GPT 3.5 answered

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.