Calculating the Capacity of a Water Tank: A Real-World Math Problem

Math questions often involve practical applications, and the calculation of how many bricks can fit into a water tank without causing it to overflow is a great example. Let's explore this problem in detail, covering the necessary calculations and providing a clear, step-by-step solution.

Understanding the Problem

The problem at hand deals with a water tank that has the dimensions of 0.8 meters high, 1.2 meters long, and 1 meter wide. The tank is currently 3/4 full of water. We need to determine how many bricks, each measuring 20 cm by 10 cm by 10 cm, can be placed in the tank before the water starts to overflow.

Step-by-Step Solution

Step 1: Calculate the Total Volume of the Tank

The first step involves calculating the total volume of the tank. The internal dimensions of the tank are:

Height: 0.8 meters Length: 1.2 meters Width: 1 meter

The formula for the volume of a rectangular tank is:

Volume Height × Length × Width

Substituting the values, we get:

Total Volume 0.8 × 1.2 × 1 0.96 m3

Step 2: Calculate the Balance Volume of the Tank

The tank is 3/4 full of water. Therefore, the remaining 1/4 of the tank is empty and can be used to place bricks without overflowing the water.

Balance Volume Total Volume × (1/4)

Balance Volume 0.96 × (1/4) 0.24 m3

Step 3: Calculate the Volume of One Brick

The dimension of each brick is 20 cm by 10 cm by 10 cm. To make the calculations easier, let's convert these measurements to meters:

Height: 20 cm 0.2 meters Length: 10 cm 0.1 meters Width: 10 cm 0.1 meters

The formula for the volume of a brick is:

Volume Height × Length × Width

Substituting the values, we get:

Volume of One Brick 0.2 × 0.1 × 0.1 0.002 m3

Step 4: Calculate the Number of Bricks That Can Be Placed

To find out how many bricks can be placed in the tank without causing water to overflow, we divide the balance volume of the tank by the volume of one brick:

No. of Bricks Balance Volume ÷ Volume of One Brick

No. of Bricks 0.24 ÷ 0.002 120

Therefore, 120 bricks can be placed in the tank without causing the water to overflow.

Alternative Method: Using Centimeters

We can also solve the problem by converting all dimensions to centimeters for easier calculations:

Height: 80 cm Length: 120 cm Width: 100 cm

The remaining space in the tank, after the 3/4 filling, is:

120 cm × 100 cm × 20 cm 240,000 cm3

The volume of one brick is:

20 cm × 10 cm × 10 cm 2,000 cm3

No. of Bricks 240,000 ÷ 2,000 120

Therefore, 120 bricks can be placed in the tank without causing the water to overflow, assuming the bricks are nonporous and do not absorb water.

Considerations and Insights

The calculation assumes the bricks are nonporous and will only displace water without absorbing it. If the bricks have a water-absorbing capacity, the available space would be slightly reduced, affecting the number of bricks that can be placed.

Conclusion

This problem highlights the practical application of volume calculations in real-world scenarios. Understanding how to calculate the balance volume of a container and the volume of individual objects is crucial for solving such problems effectively.

Keywords: water tank, volume calculation, brick capacity