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) Responses The original and replacement cones have the same volume. 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 and original cone volumes cannot be found from the information. The original cone holds more than the replacement. The original cone holds more than the replacement. The replacement cone holds more than the original.
To calculate the volume of a cone, you use the formula V = (1/3)πr^2h, 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
Therefore, the volume of the original cone is 9π cubic inches, and the volume of the replacement cone is 4π cubic inches. The original cone holds more ice cream or snow cones compared to the replacement cone.