Question

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 cone holds more than the replacement.
The replacement cone and original cone volumes cannot be found from
the information.
The replacement cone holds more than the original.
○ The original and replacement cones have the same volume.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To compare the volumes of the original and replacement cones, we can use the formula for the volume of a cone: V = (1/3) * π * r^2 * h, where r is the radius of the base and h is the height.

For the original cone:
r = 3 inches / 2 = 1.5 inches
h = 4 inches

V_original = (1/3) * π * (1.5)^2 * 4 = 9π cubic inches

For the replacement cone:
r = 4 inches / 2 = 2 inches
h = 3 inches

V_replacement = (1/3) * π * (2)^2 * 3 = 4π cubic inches

Since 9π > 4π, the original cone holds more volume than the replacement cone.

Therefore, the correct answer is:
The original cone holds more than the replacement.