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 original and replacement cones have the same volume.
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.
To calculate the volume of a cone, you can use the formula V = (1/3)πr^2h, where r is the radius of the base of the cone and h is the height of the cone.
For the original cone:
r = 6/2 = 3 inches
h = 2 inches
V = (1/3)π(3)^2(2) = 6π cubic inches
For the replacement cone:
r = 2/2 = 1 inches
h = 6 inches
V = (1/3)π(1)^2(6) = 2π cubic inches
Since 6π > 2π, the original cone has a greater volume than the replacement cone.