1 answer
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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)
The original cone holds more than the replacement.
The replacement cone and original cone volumes cannot be found from
the information.
The replacement cone holds more than the original.
The original and replacement cones have the same volume.
To calculate the volumes of the cones, we can use the formula for the volume of a cone:
Volume = 1/3 * π * r^2 * h
For the original cone with a diameter of 3 inches and a height of 4 inches, the radius (r) is half of the diameter, so r = 1.5 inches. The volume is:
Volume_original = 1/3 * π * (1.5)^2 * 4
Volume_original = 2Ï€ cubic inches
For the replacement cone with a diameter of 4 inches and a height of 3 inches, the radius (r) is half of the diameter, so r = 2 inches. The volume is:
Volume_replacement = 1/3 * π * (2)^2 * 3
Volume_replacement = 4Ï€ cubic inches
Comparing the volumes:
Volume_original = 2Ï€ cubic inches
Volume_replacement = 4Ï€ cubic inches
Since 4Ï€ is greater than 2Ï€, the replacement cone holds more than the original cone.
Therefore, the correct answer is: The replacement cone holds more than the original.