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?
To compare the volumes of the original and replacement cones, we first need to calculate their volumes using the formula for the volume of a cone:
Original cone:
Radius = 3 inches / 2 = 1.5 inches
Height = 4 inches
Volume = (1/3) * π * (1.5)^2 * 4
Volume = (1/3) * π * 2.25 * 4
Volume = (1/3) * π * 9
Volume = 3π cubic inches
Replacement cone:
Radius = 4 inches / 2 = 2 inches
Height = 3 inches
Volume = (1/3) * π * (2)^2 * 3
Volume = (1/3) * π * 4 * 3
Volume = (1/3) * π * 12
Volume = 4π cubic inches
Therefore, the volume of the original cone is 3π cubic inches, and the volume of the replacement cone is 4π cubic inches.
The volume of the replacement cone is larger than the volume of the original cone.