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 cone has a greater volume than the replacement cone. The original cone has a greater volume than the replacement cone. The original and replacement cones have the same volume. The original and replacement cones have the same volume. The replacement cone has a greater volume than the original cone.
The original and replacement cones have the same volume.
To calculate the volume of a cone, you can use the formula V = 1/3 * π * r^2 * h, where r is the radius of the base and h is the height of the cone.
For the original cone:
r = 3 inches (diameter 6 inches / 2)
h = 2 inches
V = 1/3 * π * (3)^2 * 2 = 6π cubic inches
For the replacement cone:
r = 1 inch (diameter 2 inches / 2)
h = 6 inches
V = 1/3 * π * (1)^2 * 6 = 2π cubic inches
Since 6π = 6 * 3.14 = 18.84 cubic inches and 2π = 2 * 3.14 = 6.28 cubic inches, the original and replacement cones have different volumes.
thats not one of the responses
Apologies for the oversight. Let's reassess the options given the calculations:
The original cone holds 2 times the amount as the replacement cone.
Based on the volume calculations:
Original cone volume = 6π cubic inches
Replacement cone volume = 2π cubic inches
Ratio of original cone volume to replacement cone volume:
Original cone volume / Replacement cone volume = (6π) / (2π) = 3
Therefore, the original cone holds 3 times the amount as the replacement cone, which aligns with option "The original cone holds 2 times the amount as the replacement cone." Thank you for pointing that out.
That would be wrong it should be The original cone has a greater volume than the replacement cone.
I apologize for the mistake in my response. Thank you for pointing it out. The correct comparison is that the original cone has a greater volume than the replacement cone.
The original cone has a volume of 6π cubic inches, while the replacement cone has a volume of 2π cubic inches. Since 6π is greater than 2π, the original cone indeed holds a greater volume than the replacement cone.