Okay, let's tackle this problem step by step. The question is asking for the total surface area of a cube when its volume is 1 cubic foot, and the answer needs to be in square inches. Hmm, let's start by recalling some basic formulas related to cubes.

First, I remember that the volume of a cube is calculated by side length cubed. So if the volume is 1 cubic foot, then the side length must be the cube root of 1, which is 1 foot. Wait, that seems straightforward. But the problem is asking for the surface area in square inches. So I need to convert the side length from feet to inches before calculating the surface area.

Right, since 1 foot is equal to 12 inches, the side length of the cube is 12 inches. Now, the surface area of a cube is calculated as 6 times the area of one face. Each face is a square with side length 's', so the area of one face is s squared. Therefore, the total surface area should be 6 times (s squared).

Let me write that down to keep track. Volume = s³, so s = ∛(volume). Here, volume is 1 cubic foot, so s = 1 foot. Convert s to inches: 1 foot = 12 inches. Then surface area = 6 * (12 inches)². Let me compute that. 12 squared is 144, so 6 * 144 = 864. Therefore, the total surface area should be 864 square inches.

Wait, but let me double-check to make sure I didn't skip any steps or make a conversion error. Volume is 1 cubic foot. Since 1 foot is 12 inches, 1 cubic foot is (12 inches)³, which is 1728 cubic inches. But the volume here is given as 1 cubic foot, so that's 1728 cubic inches. Wait, but the side length in inches would be 12 inches because 1 foot is 12 inches. So each side is 12 inches. Then surface area is 6*(12)^2 = 6*144=864. That seems right.

Alternatively, maybe I can compute the surface area in cubic feet first and then convert to square inches. Let me try that approach to confirm. The surface area of a cube is 6s². If the side length is 1 foot, then surface area is 6*(1)^2 = 6 square feet. Now, convert square feet to square inches. Since 1 foot is 12 inches, 1 square foot is (12 inches)^2 = 144 square inches. Therefore, 6 square feet * 144 square inches/square foot = 6*144 = 864 square inches. Yep, same result. That matches my previous calculation.

So both methods give the same answer. That gives me more confidence that 864 square inches is correct. Let me just recap the steps to ensure there's no oversight:

1. Convert the given volume from cubic feet to cubic inches if necessary. But since we're dealing with surface area, which is in square inches, we need the side length in inches. So converting the volume to determine the side length in feet first, then converting that to inches.

2. Volume of cube = s³. Given volume is 1 cubic foot, so s = 1 foot. Convert s to inches: 12 inches.

3. Surface area formula: 6s². Plug in 12 inches: 6*(12)^2 = 6*144 = 864.

Alternatively, compute surface area in cubic feet first, convert to square inches. Either way, same answer. So I think that's solid. No steps seem to be missing. The key was converting the side length from feet to inches correctly. Sometimes unit conversions can trip people up, but since 1 foot is 12 inches, multiplying by 12 each time is the right approach.

Another check: if the volume was 1 cubic foot, which is 1728 cubic inches, then the side length in inches would be the cube root of 1728, which is 12. Then surface area is 6*(12)^2=864. Same result. So that's another way to see it. Since 12^3 is 1728, that's the volume in cubic inches, so the side length is 12. Then surface area is 6*12²=864. All methods converge to 864. Therefore, I can be confident that the answer is 864 square inches.
Therefore, the total surface area of the cube is $\boxed{864}$ square inches.
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