Placing Stones in an Aquarium Without Spilling Water

Imagine an aquarium with specific dimensions: a length of 2 meters, a width of 1.5 meters, and a depth of 2.5 meters. The water level in the aquarium is at three-quarters of its depth. Now, the question is whether we can place stones with a volume of 2 cubic meters in the aquarium without spilling any water. Let's break this down step by step.

Calculating the Aquarium's Volume

First, let's determine the total volume of the aquarium. The formula for the volume of a rectangular prism (aquarium) is:

Volume Length × Breadth × Depth

Plugging in the dimensions:

Volume 2m × 1.5m × 2.5m 7.5 cubic meters

Water Level and Free Volume Calculation

The question specifies that the water level is at three-quarters of the aquarium's depth. Therefore, the volume of water is:

Volume of water 3/4 × 7.5 cubic meters 5.625 cubic meters

Now, we can find the available volume, which is the remaining space. The total volume minus the volume of water gives us:

Available volume 7.5 cubic meters - 5.625 cubic meters 1.875 cubic meters

According to another method, we can calculate one-third of the aquarium's total volume. Since the aquarium is three-quarters full:

Volume of the empty space 1/3 × 7.5 cubic meters 2.5 cubic meters

Can We Place the Stones?

Given that the volume of the stones is 2 cubic meters, and the available empty space is also 2.5 cubic meters, it is perfectly possible to place the stones without spilling water. The stones will displace water, but there is still enough space in the aquarium to accommodate them without causing overflow.

Limitations and Water Displacement

However, it's important to note that if we were to add more water to fill the aquarium completely to its full capacity, the potential for spilling would exist:

Total volume of the aquarium 7.5 cubic meters

Stones volume 2 cubic meters

Thus, the volume of water displaced (and potentially spilled) by the stones when added to a full aquarium would be:

Volume of water displaced 2 cubic meters - 1.875 cubic meters 0.125 cubic meters

Conclusion

In conclusion, placing stones with a volume of 2 cubic meters in the aquarium will not result in water spillage, given that the aquarium is already three-quarters full. This scenario highlights the importance of understanding volume calculations and water displacement in practical situations, such as aquarists and hobbyists dealing with marine environments.

Keywords

aquarium volume water displacement stone placement