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
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.