Susie runs an ice cream stand that also sells snow cones served in paper cones. The paper cones she usually uses have a diameter of 6 inches and a height of 2 inches, but her supplier is out of them. As a replacement, she purchases paper cones with a diameter of 2 inches and a height of 6 inches. How do the volumes of the original and replacement cones compare?
A. The original cone has a greater volume than the replacement cone.
B. The original cone holds 2 times the amount as the replacement cone.
C. The replacement cone has a greater volume than the original cone.
D. The original and replacement cones have the same volume./
B. The original cone holds 2 times the amount as the replacement cone.
To calculate the volume of a cone, you can use the formula V = 1/3 * π * r^2 * h, where r is the radius and h is the height.
For the original cone:
r = 3 inches (half of the diameter)
h = 2 inches
V = 1/3 * π * (3)^2 * 2 = 6π cubic inches
For the replacement cone:
r = 1 inch (half of the diameter)
h = 6 inches
V = 1/3 * π * (1)^2 * 6 = 2π cubic inches
6π / 2π = 3
Therefore, the original cone holds 3 times the amount as the replacement cone, not 2 times.