The volume of a cone is calculated using 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 = 1.5 inches (half of the diameter of 3 inches)
h = 4 inches
V = (1/3)π(1.5)^2(4) = 9π cubic inches
For the replacement cone:
r = 2 inches (half of the diameter of 4 inches)
h = 3 inches
V = (1/3)π(2)^2(3) = 4π cubic inches
Comparing the volumes:
Original cone = 9π cubic inches
Replacement cone = 4π cubic inches
Therefore, the original cone holds more volume than the replacement cone.
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 original cone holds more than the replacement. The original cone holds more than the replacement. 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 replacement cone holds more than the original.
1 answer