A cylindrical oil tank 8 ft deep holds 300300 gallons when filled to capacity. How many gallons remain in the tank when the depth of oil is 4 and one half4
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Part 1
The number of gallons remain in the tank is enter your response here.
​(Simplify your​ answer.)

To solve this problem, we need to compare the volume of oil in the tank when it is 4.5 feet full with its total capacity when it is 8 feet full. The volume of liquid in a cylindrical tank is proportional to the depth of the liquid, assuming the tank is filled uniformly.

### Step-by-step solution:

1. **Total capacity of the tank:**  
   The tank holds 300,300 gallons when it is filled to a depth of 8 feet. This represents the full capacity.

2. **Proportional relationship:**  
   Since the volume is directly proportional to the depth of the oil in the tank, we can set up a proportion based on the depth:
   
   \[
   \frac{\text{Volume of oil at 4.5 ft}}{\text{Total capacity}} = \frac{\text{Depth of oil}}{\text{Total depth}}
   \]
   \[
   \frac{V}{300,300} = \frac{4.5}{8}
   \]

3. **Solve for \( V \):**  
   Now, we can solve for the volume \( V \) of oil when the tank is 4.5 feet deep:
   
   \[
   V = 300,300 \times \frac{4.5}{8}
   \]
   
   Let’s calculate this value.

The volume of oil in the tank when the depth is 4.5 feet is 168,918.75 gallons.

To find how many gallons remain in the tank, subtract this volume from the total capacity:

\[
\text{Gallons remaining} = 300,300 - 168,918.75 = 131,381.25
\]

So, **131,381.25 gallons** remain in the tank when the depth of the oil is 4.5 feet.

Would you like more details or have any questions? Here are 5 related questions to consider:

1. How do you calculate the volume of a cylindrical tank?
2. What other shapes of tanks require different volume formulas?
3. How can the proportionality rule apply to other tank heights?
4. How does temperature affect the capacity of oil in such tanks?
5. What happens if the depth is not directly proportional to the volume?

**Tip:** Always check if a tank is perfectly cylindrical when using proportionality formulas, as irregular shapes require more complex volume calculations.

A cylindrical oil tank 8 ft deep holds 300,300 gallons when filled to capacity. How many gallons remain in the tank when the depth of oil is 4 and one half ft? (Simplify your answer.)

Learn how to calculate the remaining gallons of oil in a cylindrical tank when the depth is reduced. This problem demonstrates how to use proportions and volume formulas to solve for partial capacity in uniform tanks. Suitable for Grades 9-12 students.

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