Pete runs an ice cream stand that also sells snow cones served in paper cones. %0D%0A%0D%0AThe paper cones he usually uses have a diameter of 3 inches and a height of 4 inches, but his supplier is out of them. %0D%0A%0D%0AAs 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?%0D%0A%0D%0A(2 points)%0D%0AResponses%0D%0A%0D%0AThe replacement cone and original cone volumes cannot be found from the information.%0D%0AThe replacement cone and original cone volumes cannot be found from the information.%0D%0A%0D%0AThe original and replacement cones have the same volume.%0D%0AThe original and replacement cones have the same volume.%0D%0A%0D%0AThe replacement cone holds more than the original.%0D%0AThe replacement cone holds more than the original.%0D%0A%0D%0AThe original cone holds more than the replacement.
The original cone holds more than the replacement.
To compare the volumes of the two cones, we can use the formula for the volume of a cone: V = (1/3)πr^2h, where r is the radius and h is the height.
For the original cone with a diameter of 3 inches, the radius is 1.5 inches and the height is 4 inches. Plugging these values into the formula, we get:
V = (1/3)π(1.5)^2(4) = 9π cubic inches
For the replacement cone with a diameter of 4 inches, the radius is 2 inches and the height is 3 inches. Plugging these values into the formula, we get:
V = (1/3)π(2)^2(3) = 4π cubic inches
Since 9π is greater than 4π, the original cone holds more volume than the replacement cone.