Calculating the Volume of Water Added

Oct 13, 2025 by vinooalluri.com 130 views

Introduction

In this article, we will explore a problem involving a rectangular container and the calculation of the volume of water poured into it. The container is initially one-third filled with water, and then some water is poured into it, making it half full. We will use mathematical concepts to determine the volume of water added to the container.

Understanding the Problem

The container is a rectangular prism with dimensions 12 cm long, 8 cm wide, and 20 cm high. When it is one-third filled with water, the volume of water in the container is given by:

Volume of water = (1/3) × Length × Width × Height = (1/3) × 12 × 8 × 20 = 640 cm³

Calculating the Volume of Water Added

When the container is half filled with water, the volume of water in the container is given by:

Volume of water = (1/2) × Length × Width × Height = (1/2) × 12 × 8 × 20 = 960 cm³

Since the container was initially one-third filled with water, the volume of water added to the container is the difference between the volume of water when the container is half full and the volume of water when it is one-third full:

Volume of water added = Volume of water when half full - Volume of water when one-third full = 960 cm³ - 640 cm³ = 320 cm³

Conclusion

In this article, we have calculated the volume of water poured into a rectangular container. The container was initially one-third filled with water, and then some water was poured into it, making it half full. We used mathematical concepts to determine the volume of water added to the container. The volume of water added to the container is 320 cm³.

Mathematical Formulas Used

Volume of a rectangular prism = Length × Width × Height
Volume of water when one-third full = (1/3) × Length × Width × Height
Volume of water when half full = (1/2) × Length × Width × Height

Step-by-Step Solution

Calculate the volume of water when the container is one-third full:
- Volume of water = (1/3) × Length × Width × Height
- Volume of water = (1/3) × 12 × 8 × 20
- Volume of water = 640 cm³
Calculate the volume of water when the container is half full:
- Volume of water = (1/2) × Length × Width × Height
- Volume of water = (1/2) × 12 × 8 × 20
- Volume of water = 960 cm³
Calculate the volume of water added to the container:
- Volume of water added = Volume of water when half full - Volume of water when one-third full
- Volume of water added = 960 cm³ - 640 cm³
- Volume of water added = 320 cm³

Real-World Applications

This problem has real-world applications in various fields, such as:

Engineering: Calculating the volume of water in a container is essential in designing and building water storage systems, such as reservoirs and tanks.
Hydraulics: Understanding the volume of water in a container is crucial in designing and operating hydraulic systems, such as pumps and pipes.
Environmental Science: Calculating the volume of water in a container is essential in studying and managing water resources, such as rivers and lakes.

Conclusion

Q: What is the formula for calculating the volume of water in a container?

A: The formula for calculating the volume of water in a container is:

Volume of water = Length × Width × Height

Q: How do I calculate the volume of water when the container is one-third full?

A: To calculate the volume of water when the container is one-third full, you can use the formula:

Volume of water = (1/3) × Length × Width × Height

Q: How do I calculate the volume of water when the container is half full?

A: To calculate the volume of water when the container is half full, you can use the formula:

Volume of water = (1/2) × Length × Width × Height

Q: What is the difference between the volume of water when the container is half full and the volume of water when it is one-third full?

A: The difference between the volume of water when the container is half full and the volume of water when it is one-third full is the volume of water added to the container.

Q: How do I calculate the volume of water added to the container?

A: To calculate the volume of water added to the container, you can subtract the volume of water when the container is one-third full from the volume of water when it is half full:

Volume of water added = Volume of water when half full - Volume of water when one-third full

Q: What are some real-world applications of calculating the volume of water in a container?

A: Some real-world applications of calculating the volume of water in a container include:

Engineering: Calculating the volume of water in a container is essential in designing and building water storage systems, such as reservoirs and tanks.
Hydraulics: Understanding the volume of water in a container is crucial in designing and operating hydraulic systems, such as pumps and pipes.
Environmental Science: Calculating the volume of water in a container is essential in studying and managing water resources, such as rivers and lakes.

Q: What are some common mistakes to avoid when calculating the volume of water in a container?

A: Some common mistakes to avoid when calculating the volume of water in a container include:

Incorrectly measuring the dimensions of the container: Make sure to measure the length, width, and height of the container accurately.
Forgetting to account for the volume of water already in the container: Make sure to subtract the volume of water already in the container from the total volume of water.
Not using the correct formula: Make sure to use the correct formula for calculating the volume of water in a container.

Q: How can I practice calculating the volume of water in a container?

A: You can practice calculating the volume of water in a container by:

Using online calculators: There are many online calculators available that can help you calculate the volume of water in a container.
Working with real-world examples: Try calculating the volume of water in a container using real-world examples, such as a swimming pool or a water tank.
Practicing with different dimensions: Try calculating the volume of water in a container using different dimensions, such as a container with a length of 10 cm and a width of 5 cm.

Conclusion

Calculating the volume of water in a container is an essential skill that has many real-world applications. By understanding the formula for calculating the volume of water in a container and avoiding common mistakes, you can accurately calculate the volume of water in a container. Practice calculating the volume of water in a container using online calculators, real-world examples, and different dimensions to become proficient in this skill.