Determining the Full Capacity of a Tank When It Contains a Specific Volume at 3/4 Full

When dealing with tanks and their capacity, it is crucial to understand how to calculate the full capacity based on a known volume at a certain fraction of its full capacity. This article will guide you through the process using a practical example involving a tank that contains 60 liters of water when 3/4 full.

Understanding the Problem

A tank that is 3/4 full contains 60 liters of water. To determine the full capacity of the tank, we need to set up an equation based on the given information. Let's denote the full capacity of the tank as x liters.

Setting Up the Equation

The equation to solve is:

To find the full capacity x, we can multiply both sides of the equation by the reciprocal of 3/4, which is 4/3:

Therefore, the full capacity of the tank is 80 liters.

Further Analysis and Verification

To further verify this calculation, we can use the following method to ensure accuracy:

Verification Method 1

Divide 60 liters by 3 to get 20 liters, which represents 1/4 of the tank’s capacity. Since 4/4 (or 1) of the tank would be 4 times 20 liters, the full capacity of the tank is:

4 x 20 80 liters

This confirms the full capacity of the tank is indeed 80 liters.

Verification Method 2

If we consider the tank being 50% full and containing 100 liters of water, we can work backwards to determine the full capacity. Since 50% represents half of the tank, the full capacity would be:

100 liters x 2 200 liters

However, this seems to be an incorrect approach as it does not align with the initial 3/4 full scenario. The correct interpretation of the problem is to use the 3/4 full information only.

Verification Method 3

Another method uses algebraic calculation:

Solving for v (full volume), we get:

This method also yields 200 liters as the full capacity, which is incorrect based on the 3/4 full scenario.

Conclusion

The correct and simplest method is to use the initial 3/4 full information. The tank's full capacity is 80 liters. It's important to recognize that different scenarios (e.g., 50% full) do not align with the 3/4 full condition and should be treated separately.

Keywords

Tank Capacity Calculation, Volume Determination, Mathematical Problem Solving