Question 3

The height of the can is 4.1 inches.

To find the height of the can, we first determine the volume it holds. Since the can holds 2.0 cups of water and each cup is 14.4 cubic inches, the total volume is 28.8 cubic inches. Using the formula for the volume of a cylinder, V = πr²h, where r is the radius, we can solve for the height.

A) 1

This option suggests that the height of the can is 1 inch. However, given that the can holds 28.8 cubic inches of water and the diameter is 3.0 inches (which gives a radius of 1.5 inches), a height of only 1 inch would result in a volume much less than 28.8 cubic inches. Thus, this option is incorrect.

B) 2

A height of 2 inches would also provide an insufficient volume. Calculating the volume using the formula V = π(1.5)²(2), we find it is approximately 14.1 cubic inches, which is far less than the 28.8 cubic inches required for the can. Therefore, this option is incorrect.

C) 3.1

While a height of 3.1 inches increases the volume, it still does not meet the requirement. Plugging 3.1 inches into the volume formula yields approximately 21.9 cubic inches, which is still short of the necessary 28.8 cubic inches. Thus, this option is also incorrect.

D) 4.1

This option is correct. By substituting 4.1 inches into the volume formula, V = π(1.5)²(4.1), we calculate the volume to be approximately 28.8 cubic inches, which matches the required volume for the can. Therefore, this option is valid.

E) 6.2

A height of 6.2 inches results in a volume that significantly exceeds the required amount. Calculating this yields a volume of approximately 44.5 cubic inches, which is much larger than 28.8 cubic inches. Hence, this option is incorrect.

Conclusion

The height of the can being 4.1 inches accurately fulfills the volume requirement of 28.8 cubic inches. All other options fail to provide a sufficient volume based on the given dimensions of the can, confirming that D is the only correct choice.