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The problem in the image involves calculating the pressure required to compress 5600 liters (L) of air into a spherical air tank for a deep-sea submersible. Here’s a breakdown:

### Given dataThe problem in the image involves calculating the pressure required to compress 5600 liters (L) of air into a spherical air tank for a deep-sea submersible. Here’s a breakdown:

### Given 
1. The **volume of air** required: \( V_1 = 5600 \, \text{L} \)
2. The **tank diameter**: \( d = 84.0 \, \text{cm} \)
   - This can be converted to the tank's radius: \( r = \frac{d}{2} = 42.0 \, \text{cm} \)
   - Convert this to meters: \( r = 0.42 \, \text{m} \)
3. The **volume of the tank** can be calculated using the formula for the volume of a sphere: 
   \[
   V_2 = \frac{4}{3} \pi r^3
   \]
   Substituting \( r = 0.42 \, \text{m} \), we can find the volume of the tank in cubic meters (m³), then convert it to liters (L) as \( 1 \, \text{m}^3 = 1000 \, \text{L} \).

4. We’ll use **Boyle's Law** to find the pressure:
   \[
   P_1 V_1 = P_2 V_2
   \]
   Assuming the initial pressure \( P_1 \) is 1 atmosphere (atm), we solve for the final pressure \( P_2 \) using the volumes \( V_1 \) and \( V_2 \).

Let me perform the calculations to find the required pressure \( P_2 \).The pressure required to compress 5600 liters of air into the spherical air tank is approximately **18.0 atm**. The volume of the tank is about **310.34 liters**.

Would you like further details or have any questions?

Here are five related questions to expand this problem:

1. How does Boyle's Law apply to different gas mixtures in deep-sea environments?
2. What safety factors should be considered when compressing gases to high pressures?
3. How would the pressure change if the air tank were smaller or larger?
4. What happens to the gas temperature during compression, and how can it be managed?
5. How would the use of non-spherical tanks affect pressure calculations?

**Tip:** Always ensure your significant figures reflect the precision of your initial measurements for accurate results.

A marine biologist is preparing a deep-sea submersible for a dive. The sub stores breathing air under high pressure in a spherical air tank that measures 84.0 cm wide. The biologist estimates she will need 5600 L of air for the dive. Calculate the pressure to which this volume of air must be compressed in order to fit into the air tank. Write your answer in atmospheres.

Learn how to calculate the pressure needed to compress 5600 L of air into a spherical tank for a deep-sea submersible. This problem covers Boyle's Law and the formula for the volume of a sphere, ideal for students in Grades 9-12.

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