Calculating Water Levels in a Rectangular Tank

Do you often find yourself wondering how to determine the water level in a rectangular tank? This article will walk you through the process of finding the depth of water in a tank that is initially three-quarters filled, and then further filled with 4000 liters of water.

Understanding the Tank Dimensions

Our rectangular tank measures 4 meters in length, 2 meters in width, and 4.8 meters in height. When fully filled, the tank can hold a volume of 38.4 cubic meters of water, which is equivalent to 38,400 liters of water (since 1 cubic meter 1000 liters).

Initial Water Level

The tank is initially three-quarters filled with water. This means the height of the water is 0.75 times the height of the tank:

Initial Water Height 4.8 meters times; 0.75 3.6 meters

We can also verify this by calculating the volume of water in the tank initially:

Initial Volume of Water 4 meters times; 2 meters times; 3.6 meters 28.8 cubic meters

Converting this to liters, we get:

Initial Volume of Water 28.8 cubic meters times; 1000 liters/cubic meter 28,800 liters

Adding More Water to the Tank

Now, let's consider adding 4000 liters of water to the tank. The total volume of water after adding 4000 liters is:

Total Volume of Water 28,800 liters 4000 liters 32,800 liters

To find the new water height, we start by calculating the volume per meter of water in the tank:

Volume per Meter 38,400 liters / 4.8 meters 8000 liters/meter

Using this, we can determine the new water height:

New Water Height 32,800 liters / 8000 liters/meter 4.1 meters

Final Water Level and Tank Capacity

With this calculation, we find that the new water level in the tank is 4.1 meters. This is 0.7 meters from the top of the tank. The total amount of water now stored in the tank is 32,800 liters, or 85.416% of the full capacity of 38,400 liters.

Summary of Key Calculations

Initial Volume of Water: 38,400 liters * 0.75 28,800 liters Volume per Meter of Water: 38,400 liters / 4.8 meters 8000 liters/meter New Water Level: 32,800 liters / 8000 liters/meter 4.1 meters

In conclusion, understanding the dimensions and volume of a rectangular tank is crucial for accurately determining the water level. This method can be applied to various situations, such as calculating water in reservoirs, water tanks, and other similar structures.