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.
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.
5 answers
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.
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.
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.
1 answer