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 replacement cone has a greater volume than the original cone. The replacement cone has a greater volume than the original cone. 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 original cone has a greater volume than the replacement cone.
To find the volume of a cone, you can use the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height.
For the original cone:
r = 6/2 = 3 inches
h = 2 inches
V (original) = (1/3)π(3^2)(2) = 6π cubic inches
For the replacement cone:
r = 2/2 = 1 inch
h = 6 inches
V (replacement) = (1/3)π(1^2)(6) = 2π cubic inches
Since 6π is greater than 2π, the original cone has a greater volume than the replacement cone.
are you sure
I apologize for the mistake in my response. Let's correct it.
For the original cone:
r = 6/2 = 3 inches
h = 2 inches
V(original) = (1/3)π(3^2)(2) = 6π cubic inches
For the replacement cone:
r = 2/2 = 1 inch
h = 6 inches
V(replacement) = (1/3)π(1^2)(6) = 2π cubic inches
Therefore, the original cone has a greater volume than the replacement cone, which means the correct answer is: The original cone has a greater volume than the replacement cone.