Rowan is taking his siblings to get ice cream. They can't decide whether to get a cone or a cup because they want to get the most ice cream for their money. If w = 3 in, x = 6 in, y = 6 in, z = 3 in, and the cone and cup are filled evenly to the top with no overlap, which container will hold the most ice cream? Use 3.14 for π, and round your answer to the nearest tenth.

a cone with a height of x and a radius of w, a cylinder with a diameter of y and a height of z

The cup holds 84.8 in3 more ice cream than the cone.

The cone holds 84.8 in3 more ice cream than the cup.

The cup holds 28.3 in3 more ice cream than the cone.

The cone holds 28.3 in3 more ice cream than the cup.

Question:

Rowan is taking his siblings to get ice cream. They can't decide whether to get a cone or a cup because they want to get the most ice cream for their money. If w = 2.5 in, x = 5 in, y = 5 in, z = 3 in, and the cone and cup are filled evenly to the top with no overlap, which container will hold the most ice cream? Use 3.14 for π, and round your answer to the nearest tenth.

Answer: The cup holds 26.2 in3 more ice cream than the cone.

The correct answer is C. The cup holds 28.3 in³ more ice cream than the cone.

Step-by-step explanation:

1. Let's find the volume of ice cream that the cone holds, this way:

Volume = π * r² * h/3

Replacing with the real values, we have:

Volume = 3.14 * 3² * 6/3

Volume = 3.14 * 9 * 2 = 56.5 inches³

2. Let's find the volume of ice cream that the cup holds, this way:

Volume = π * r² * h

Diameter = 6 inches ⇒ Radius = 3 inches

Replacing with the real values, we have:

Volume = 3.14 * 3² * 3

Volume = 3.14 * 9 * 3 = 84.8 inches³

3. Let's find the difference, this way:

Volume of the cup - volume of the cone = 84.8 - 56.5 = 28.3 inches³

The correct answer is C. The cup holds 28.3 in³ more ice cream than the cone