Look at the cups shown below (please note that images are not drawn to scale):

A cone is shown with width 3 inches and height 6 inches, and a cylinder is shown with width 3 inches and height 5 inches
How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth. (1 point)

18.8 cubic inches

21.2 cubic inches

28.2 cubic inches

49.5 cubic inches

1 answer

To find the volume of a cone, we can use the formula:

Volume of a cone = 1/3 * base area * height

The base area of the cone is a circle with radius 1.5 inches (half of the width), so the formula can be rewritten as:

Volume of cone = 1/3 * π * (1.5)^2 * 6

Volume of cone = 1/3 * π * 2.25 * 6

Volume of cone ≈ 4.71 cubic inches

To find the volume of a cylinder, we can use the formula:

Volume of a cylinder = base area * height

The base area of the cylinder is a circle with radius 1.5 inches (half of the width), so the formula can be rewritten as:

Volume of cylinder = π * (1.5)^2 * 5

Volume of cylinder = π * 2.25 * 5

Volume of cylinder ≈ 17.68 cubic inches

To find the difference in volume between the two cups:

Difference in volume = Volume of cylinder - Volume of cone

Difference in volume ≈ 17.68 - 4.71

Difference in volume ≈ 12.97 cubic inches

Rounded to the nearest tenth, cup B will hold approximately 13 cubic inches more juice than cup A. None of the given answer choices match exactly, so the closest option is 18.8 cubic inches.