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 approximately 4.1 inches.

To find the height of the can, we first calculate its volume using the amount of water it holds. Since the can holds 2.0 cups of water, we convert this to cubic inches and then use the formula for the volume of a cylinder to find the height.

A (1) YOUR ANSWER

Choosing a height of 1 inch would imply a very small volume for the can. The formula for the volume of a cylinder (V = πr²h) shows that a height of 1 inch cannot accommodate the volume of 2 cups (which is 28.8 cubic inches), thus making this option incorrect.

B (2) YOUR ANSWER

A height of 2 inches also fails to provide enough volume for the can. Using the same volume formula, a cylindrical can with a height of 2 inches and a diameter of 3 inches yields a volume far less than the required 28.8 cubic inches, confirming that this choice is incorrect.

C (3.1) YOUR ANSWER

While a height of 3.1 inches comes closer, it still does not reach the necessary volume. The calculated volume for this height would still fall short of 28.8 cubic inches, indicating that this option does not meet the requirement for the can's capacity.

D (4.1) CORRECT

This height is indeed correct. With a diameter of 3 inches, the radius is 1.5 inches. Calculating the volume with a height of 4.1 inches yields a volume of approximately 28.8 cubic inches, matching the capacity of 2 cups of water.

E (6.2) YOUR ANSWER

A height of 6.2 inches results in a volume that exceeds the required 28.8 cubic inches. Although it is a valid calculation, it is larger than necessary, making this option incorrect.

Conclusion

To determine the height of a cylindrical can that holds 2 cups of water, we calculated the necessary volume and applied the formula for the volume of a cylinder. The only option that accurately meets the volume requirement is approximately 4.1 inches, ensuring the can can hold the specified amount of liquid without exceeding its capacity.