Each side of a cube is measured to be 7.241 m. Find its total surface area to correct number of significant figures.

Answer

To find the total surface area of a cube when each side is measured to be 7.241 m, we can follow these steps:

### Step 1: Identify the formula for the surface area of a cube.
The total surface area (SA) of a cube is given by the formula:
\[ SA = 6a^2 \]
where \( a \) is the length of one side of the cube.

### Step 2: Substitute the given value into the formula.
In this case, the length of each side \( a \) is 7.241 m. We can substitute this value into the formula:
\[ SA = 6 \times (7.241 \, \text{m})^2 \]

### Step 3: Calculate \( a^2 \).
First, we need to calculate \( (7.241)^2 \):
\[ (7.241)^2 = 52.619881 \, \text{m}^2 \]

### Step 4: Multiply by 6 to find the total surface area.
Now, we multiply this result by 6:
\[ SA = 6 \times 52.619881 \, \text{m}^2 = 315.719286 \, \text{m}^2 \]

### Step 5: Round the result to the correct number of significant figures.
The original measurement of the side (7.241 m) has 4 significant figures. Therefore, we need to round the total surface area to 4 significant figures:
- The calculated surface area is 315.719286 m².
- The first four significant figures are 3157.
- The fifth digit is 1, which is less than 5, so we do not round up.

Thus, the total surface area of the cube, rounded to the correct number of significant figures, is:
\[ SA = 315.7 \, \text{m}^2 \]

### Final Answer:
The total surface area of the cube is \( 315.7 \, \text{m}^2 \).

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