Pete runs an ice cream stand that also sells snow cones served in paper
cones.
The paper cones he usually uses have a diameter of 3 inches and a height
of 4 inches, but his supplier is out of them.
As a replacement, he purchases paper cones with a diameter of 4 inches
and a height of 3 inches. How do the volumes of the original and
replacement cones compare?
(2 points)
The original and replacement cones have the same volume.
The original cone holds more than the replacement.
The replacement cone holds more than the original.
The replacement cone and original cone volumes cannot be found from
the information.
To find the volume of a cone, we use the formula V = 1/3 * π * r^2 * h, where r is the radius of the base of the cone and h is the height of the cone.
For the original cone:
r = 1.5 inches, h = 4 inches
V = 1/3 * π * (1.5)^2 * 4
V = 1/3 * π * 2.25 * 4
V = π * 3 * 4
V = 12π cubic inches
For the replacement cone:
r = 2 inches, h = 3 inches
V = 1/3 * π * 2^2 * 3
V = 1/3 * π * 4 * 3
V = 4π cubic inches
The volume of the original cone is 12π cubic inches, and the volume of the replacement cone is 4π cubic inches.
Therefore, the original cone holds more than the replacement cone. The correct answer is:
The original cone holds more than the replacement.