The volume of 1 cup of water is 14.4 cubic inches. The diameter of an empty cylindrical can is 3.0 inches. The can holds 2.0 cups of water. What is the height of the can, to the nearest 0.1 inch?

Rationale

The height of the can is 4.1 inches.

To find the height of the can, we first calculate its volume using the given measurements. Since the can holds 2.0 cups of water, we convert this to cubic inches (2.0 cups × 14.4 cubic inches/cup = 28.8 cubic inches). Using the volume formula for a cylinder (V = πr²h), we can solve for height (h) once we have the radius (r) from the diameter.

A (1) YOUR ANSWER

This choice suggests a height that is significantly smaller than the calculated height. Given the can's volume of 28.8 cubic inches and the diameter of 3.0 inches, a height of 1 inch would produce an insufficient volume, as V = π(1.5)²(1) = approximately 7.07 cubic inches, which is far less than 28.8 cubic inches.

B (2) YOUR ANSWER

A height of 2 inches also results in too low a volume. Using the formula for the volume of a cylinder, V = π(1.5)²(2) gives approximately 14.14 cubic inches, which again does not meet the required volume of 28.8 cubic inches.

C (3.1) YOUR ANSWER

This choice yields a volume closer to the required amount but still falls short. Calculating V = π(1.5)²(3.1) results in approximately 21.73 cubic inches. While this is an improvement, it still does not reach the needed volume of 28.8 cubic inches.

D (4.1) CORRECT

This choice is correct. When calculating V = π(1.5)²(4.1), we find a volume of approximately 29.0 cubic inches, which is nearly equal to the required volume of 28.8 cubic inches, confirming the height of the can.

E (6.2) YOUR ANSWER

A height of 6.2 inches would yield an excessively large volume. The calculation V = π(1.5)²(6.2) results in approximately 43.96 cubic inches, which greatly exceeds the can's capacity of 28.8 cubic inches.

Conclusion

The height of the can is determined by using the volume formula for a cylinder and the relationship between the volume of water it holds and its dimensions. After evaluating all choices, 4.1 inches is the only option that accurately meets the volume requirement while maintaining the cylindrical shape defined by the given diameter.