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?
A. The original cone holds more than the replacement.
B. The replacement cone holds more than the original.
C. The replacement cone and original cone volumes cannot be found from the information.
D. The original and replacement cones have the same volume.
B. The replacement cone holds more than the original.
To compare the volumes of the cones, we can use the formula for the volume of a cone, which is V = (1/3)πr^2h, where r is the radius of the base and h is the height.
For the original cone:
r = 3/2 = 1.5 inches
h = 4 inches
V_original = (1/3)π(1.5)^2(4) = 9π cubic inches
For the replacement cone:
r = 4/2 = 2 inches
h = 3 inches
V_replacement = (1/3)π(2)^2(3) = 4π cubic inches
Therefore, the replacement cone holds more volume than the original cone.