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?
To find the volume of a cone, you can use the formula V = (1/3)πr²h, where r is the radius and h is the height.
For the original cone, with a diameter of 6 inches, the radius would be 6/2 = 3 inches. Therefore, the volume of the original cone would be V = (1/3)π(3)²(2) = 6π cubic inches.
For the replacement cone, with a diameter of 2 inches, the radius would be 2/2 = 1 inch. Therefore, the volume of the replacement cone would be V = (1/3)π(1)²(6) = 2π cubic inches.
Comparing the volumes of the original and the replacement cone:
Original cone volume: 6π cubic inches
Replacement cone volume: 2π cubic inches
The original cone's volume is three times larger than the replacement cone's volume.