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The problem in the image is in Spanish and it asks:

"A cylindrical tube made of brass with a length of 1.28 m, sealed on one end, is filled with mercury. It is determined that the mass of mercury needed to fill the tube is 38.6 × 10⁻³ kg. The density of mercury is 13,690 kg/m³. Calculate the inner diameter of the brass tube in meters and express your answer using scientific notation."

To solve this:

### Step 1: Volume of mercury in the tube
We are given the mass of the mercury and its density. The volume \( V \) of the mercury can be found using the formula:
\[
V = \frac{m}{\rho}
\]
where:
- \( m = 38.6 \times 10^{-3} \, \text{kg} \) is the mass of the mercury,
- \( \rho = 13,690 \, \text{kg/m}^3 \) is the density of mercury.

### Step 2: Relationship between volume and tube dimensions
The volume of the cylindrical tube filled with mercury is also given by:
\[
V = \pi \left(\frac{d}{2}\right)^2 L
\]
where:
- \( d \) is the inner diameter of the tube (what we are solving for),
- \( L = 1.28 \, \text{m} \) is the length of the tube.

### Step 3: Equate both volume expressions
Now we equate both expressions for volume and solve for the diameter \( d \).

Let me calculate this for you.It seems there's a temporary issue with the calculation. However, I will outline the steps to help you complete the solution manually.

1. **Volume of mercury:**
   \[
   V = \frac{38.6 \times 10^{-3}}{13,690} \, \text{m}^3
   \]
   Calculate this volume.

2. **Inner diameter:**
   Rearranging the volume formula for the tube to solve for \( d \):
   \[
   d = 2 \times \sqrt{\frac{V}{\pi \times 1.28}}
   \]
   where \( V \) is the volume from the previous step. Compute the result to find the inner diameter.

You can apply these steps, and the answer should be in scientific notation. Let me know if you have any questions, or if you would like further assistance!

Here are 5 related questions to consider:
1. How does the density of a liquid affect the volume it occupies?
2. How would the result change if the length of the tube were doubled?
3. Can the diameter be calculated if the tube were not cylindrical?
4. What happens to the volume formula if the tube is not fully filled?
5. How can you convert between units of density (e.g., kg/m³ to g/cm³)?

**Tip:** Ensure that you always match units correctly when working with mass, volume, and density calculations to avoid errors.

Un tubo cilíndrico de latón con una longitud de 1.28 m, sellado en un extremo, se llena con mercurio. Se determina que la masa de mercurio necesaria para llenar el tubo es de 38.6 × 10⁻³ kg. La densidad del mercurio es de 13,690 kg/m³. Calcula el diámetro interior del tubo de mercurio y expresa su valor usando notación científica.

Aprende a calcular el diámetro interior de un tubo cilíndrico de latón lleno de mercurio, con una longitud de 1.28 m y una masa de 38.6 × 10⁻³ kg. La densidad del mercurio es de 13,690 kg/m³. Sigue los pasos y fórmulas necesarias para resolver el problema y expresar la respuesta en notación científica.

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