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 original and replacement cones have the same volume.
The replacement cone and original cone volumes cannot be found from the information.
The replacement cone holds more than the original.
To compare the volumes of the original and replacement cones, we can use the formula for the volume of a cone:
Volume of a cone = (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:
Radius (r) = 3 inches / 2 = 1.5 inches.
Height (h) = 4 inches.
Volume of the original cone = (1/3) * π * (1.5)^2 * 4 = 9π cubic inches.
For the replacement cone:
Radius (r) = 4 inches / 2 = 2 inches.
Height (h) = 3 inches.
Volume of the replacement cone = (1/3) * π * (2)^2 * 3 = 4π cubic inches.
Therefore, the original cone holds more ice cream/snow cone than the replacement cone.