The edges of a shoebox are measured to be 12.6 cm, 18.8 cm, and 29 cm. Determine the volume of the box retaining the proper number of significant figures in your answer.

To determine the volume of the shoebox and retain the proper number of significant figures, we will follow these steps:

### Step 1: Calculate the Volume
The volume \( V \) of a rectangular box can be calculated using the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
Here, the given dimensions are:
- Length = \( 12.6 \) cm
- Width = \( 18.8 \) cm
- Height = \( 29.0 \) cm

So,
\[
V = 12.6 \times 18.8 \times 29.0
\]

### Step 2: Perform the Multiplication
First, calculate the product:
\[
V = 12.6 \times 18.8 \times 29.0 = 6862.32 \text{ cm}^3
\]

### Step 3: Determine Significant Figures
The number of significant figures in the measurements are:
- 12.6 cm has 3 significant figures
- 18.8 cm has 3 significant figures
- 29.0 cm has 3 significant figures

The result should be rounded to 3 significant figures since that is the smallest number of significant figures in the measurements.

### Step 4: Round the Result
Rounding \( 6862.32 \) cm³ to 3 significant figures gives:
\[
V \approx 6860 \text{ cm}^3
\]

Thus, the volume of the shoebox is **6860 cm³**.

Would you like further details on significant figures or anything else? Here are five related questions:

1. How would the volume change if the dimensions were measured as 12.60 cm, 18.80 cm, and 29.00 cm?
2. What is the volume of the shoebox in liters, retaining the correct significant figures?
3. How does the number of significant figures affect the accuracy of the volume calculation?
4. How do you calculate the surface area of the shoebox, and what are the significant figures in that result?
5. If the shoebox dimensions were given in meters, how would you convert and calculate the volume in cubic centimeters?

**Tip:** Always ensure that the final answer is rounded according to the measurement with the least number of significant figures.

Learn how to calculate the volume of a shoebox with dimensions 12.6 cm, 18.8 cm, and 29.0 cm, retaining 3 significant figures. This problem involves basic geometry and measurement concepts, focusing on significant figures in scientific calculations. Suitable for high school students.

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