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)
Responses
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.
D. The original and replacement cones have the same volume.
To calculate the volume of a cone, you can use the formula V = (1/3)πr^2h, where r is the radius of the base and h is the height of the cone.
For the original cone:
r = 3/2 = 1.5 inches
h = 4 inches
V_original = (1/3)π(1.5)^2(4) = (1/3)π(2.25)(4) = 3π
For the replacement cone:
r = 4/2 = 2 inches
h = 3 inches
V_replacement = (1/3)π(2)^2(3) = (1/3)π(4)(3) = 4π
Since 3π is equal to 4π, the original and replacement cones have the same volume.