25. 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?
Answer: D
The height of the can is 4.1 inches.
To determine the height of the can, we first calculate the volume it holds in cubic inches by multiplying the volume of one cup by the number of cups the can holds. Since the can holds 2.0 cups, the total volume is 28.8 cubic inches. Using the formula for the volume of a cylinder, we can find the height.
A) 1
This option suggests that the height of the can is 1 inch. Given that the can holds a volume of 28.8 cubic inches and the diameter is 3.0 inches, a height of 1 inch would result in a far smaller volume than required. Therefore, this option is incorrect.
B) 2
A height of 2 inches also fails to provide sufficient volume. With the diameter of 3.0 inches, the volume of a cylinder with this height would not meet the required 28.8 cubic inches. Thus, this option is incorrect.
C) 3.1
Choosing a height of 3.1 inches still does not yield the necessary volume. The calculated volume using this height does not reach 28.8 cubic inches, indicating that this option is also incorrect.
D) 4.1
This option provides a height of 4.1 inches, which, when calculated using the formula for the volume of a cylinder (V = πr²h), results in the correct total volume of 28.8 cubic inches. Therefore, this option is correct.
E) 6.2
A height of 6.2 inches would result in a volume that exceeds the required 28.8 cubic inches significantly. Thus, this option is incorrect.
Conclusion
The correct height of the can is 4.1 inches, as it accurately corresponds to the required volume of 28.8 cubic inches based on the given diameter. All other options fail to meet the necessary volume calculations, confirming that they are incorrect.