Question

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?

a The original cone has a greater volume than the replacement cone.
b. The replacement cone has a greater volume than the original cone.
c. The original cone holds 2 times the amount as the replacement cone.
d. The original and replacement cones have the same volume.

Answer 1

By calculating the volumes of the cones using the formula for the volume of a cone, we find that the replacement cone with a diameter of 4 inches and a height of 3 inches has a greater volume than the original cone with a diameter of 3 inches and a height of 4 inches.

Step-by-step explanation:

To compare the volumes of Pete's original and replacement paper cones for his ice cream stand, we can use the formula for the volume of a cone, which is V = 1/3 πr^2 h, where V is the volume, r is the radius, and h is the height. The original cones have a diameter of 3 inches (radius 1.5 inches) and a height of 4 inches, while the replacement cones have a diameter of 4 inches (radius 2 inches) and a height of 3 inches.

Calculating the volumes:

• Original cone volume: V1 = 1/3 π (1.5)^2 × 4 ≈ 9.42 inches^3
• Replacement cone volume: V2 = 1/3 π (2)^2 × 3 ≈ 12.57 inches^3

Therefore, the replacement cone actually has a greater volume than the original cone. The correct answer is (b) The replacement cone has a greater volume than the original cone.