Find The Value Of A Cuboid With Length 45 CM Bread 10 Cm And Height 20 Cm Long How To Solve It
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Introduction
In geometry, a cuboid is a three-dimensional shape with six rectangular faces. It is also known as a rectangular prism. The volume of a cuboid is an essential concept in mathematics, and it has numerous real-world applications in fields such as architecture, engineering, and design. In this article, we will explore how to find the volume of a cuboid with a length of 45 cm, a breadth of 10 cm, and a height of 20 cm.
Understanding the Formula
The formula to find the volume of a cuboid is:
Volume = Length × Breadth × Height
This formula is derived from the fact that the volume of a cuboid is equal to the product of its length, breadth, and height. The length, breadth, and height are the three dimensions of the cuboid, and they are measured in the same units (e.g., centimeters, meters, etc.).
Applying the Formula
Now that we have the formula, let's apply it to find the volume of the cuboid with a length of 45 cm, a breadth of 10 cm, and a height of 20 cm.
Length (l) = 45 cm Breadth (b) = 10 cm Height (h) = 20 cm
Using the formula, we can calculate the volume as follows:
Volume = l × b × h Volume = 45 × 10 × 20 Volume = 9000 cubic centimeters
Converting Units
In the previous example, we calculated the volume in cubic centimeters (cm³). However, in many real-world applications, it is more convenient to express the volume in cubic meters (m³). To convert the volume from cubic centimeters to cubic meters, we can use the following conversion factor:
1 cubic meter = 1,000,000 cubic centimeters
Using this conversion factor, we can convert the volume of the cuboid from cubic centimeters to cubic meters as follows:
Volume (cm³) = 9000 cubic centimeters Volume (m³) = 9000 ÷ 1,000,000 Volume (m³) = 0.009 cubic meters
Real-World Applications
The concept of finding the volume of a cuboid has numerous real-world applications in fields such as:
- Architecture: Architects use the volume of a cuboid to calculate the amount of materials required for building construction.
- Engineering: Engineers use the volume of a cuboid to design and optimize the size and shape of containers, tanks, and other storage vessels.
- Design: Designers use the volume of a cuboid to create 3D models and prototypes of products and packaging.
Conclusion
In conclusion, finding the volume of a cuboid is a simple yet essential concept in mathematics. By applying the formula Volume = Length × Breadth × Height, we can calculate the volume of a cuboid with ease. Whether you are an architect, engineer, designer, or simply a math enthusiast, understanding the concept of finding the volume of a cuboid is crucial for solving problems and making informed decisions in various fields.
Frequently Asked Questions
Q: What is the formula to find the volume of a cuboid?
A: The formula to find the volume of a cuboid is Volume = Length × Breadth × Height.
Q: How do I convert the volume of a cuboid from cubic centimeters to cubic meters?
A: To convert the volume of a cuboid from cubic centimeters to cubic meters, you can use the following conversion factor: 1 cubic meter = 1,000,000 cubic centimeters.
Q: What are some real-world applications of finding the volume of a cuboid?
A: Some real-world applications of finding the volume of a cuboid include architecture, engineering, and design.
Additional Resources
For more information on finding the volume of a cuboid, you can refer to the following resources:
- Mathematics textbooks: Many mathematics textbooks cover the concept of finding the volume of a cuboid in detail.
- Online tutorials: Websites such as Khan Academy and Mathway offer interactive tutorials and exercises on finding the volume of a cuboid.
- Mathematical software: Software such as GeoGebra and Mathematica can be used to visualize and calculate the volume of a cuboid.
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Q: What is a cuboid?
A cuboid is a three-dimensional shape with six rectangular faces. It is also known as a rectangular prism. Cuboids are commonly used in architecture, engineering, and design to create buildings, containers, and other structures.
Q: What is the formula to find the volume of a cuboid?
The formula to find the volume of a cuboid is:
Volume = Length × Breadth × Height
This formula is derived from the fact that the volume of a cuboid is equal to the product of its length, breadth, and height.
Q: How do I convert the volume of a cuboid from cubic centimeters to cubic meters?
To convert the volume of a cuboid from cubic centimeters to cubic meters, you can use the following conversion factor:
1 cubic meter = 1,000,000 cubic centimeters
For example, if the volume of a cuboid is 9000 cubic centimeters, you can convert it to cubic meters as follows:
Volume (cm³) = 9000 cubic centimeters Volume (m³) = 9000 ÷ 1,000,000 Volume (m³) = 0.009 cubic meters
Q: What are some real-world applications of finding the volume of a cuboid?
Some real-world applications of finding the volume of a cuboid include:
- Architecture: Architects use the volume of a cuboid to calculate the amount of materials required for building construction.
- Engineering: Engineers use the volume of a cuboid to design and optimize the size and shape of containers, tanks, and other storage vessels.
- Design: Designers use the volume of a cuboid to create 3D models and prototypes of products and packaging.
Q: How do I find the volume of a cuboid with a length of 50 cm, a breadth of 15 cm, and a height of 25 cm?
To find the volume of a cuboid with a length of 50 cm, a breadth of 15 cm, and a height of 25 cm, you can use the formula:
Volume = Length × Breadth × Height Volume = 50 × 15 × 25 Volume = 18750 cubic centimeters
Q: Can I use the formula to find the volume of a cuboid with a length of 2 meters, a breadth of 1.5 meters, and a height of 3 meters?
Yes, you can use the formula to find the volume of a cuboid with a length of 2 meters, a breadth of 1.5 meters, and a height of 3 meters. First, convert the length, breadth, and height to the same units (e.g., centimeters). Then, use the formula:
Volume = Length × Breadth × Height Volume = 200 × 150 × 300 Volume = 9000000 cubic centimeters
Q: What is the difference between a cuboid and a rectangular prism?
A cuboid and a rectangular prism are the same thing. The term "cuboid" is commonly used in the UK and Australia, while the term "rectangular prism" is commonly used in the US.
Q: Can I use the formula to find the volume of a cuboid with a length of 10 inches, a breadth of 8 inches, and a height of 12 inches?
Yes, you can use the formula to find the volume of a cuboid with a length of 10 inches, a breadth of 8 inches, and a height of 12 inches. First, convert the length, breadth, and height to the same units (e.g., centimeters). Then, use the formula:
Volume = Length × Breadth × Height Volume = 25.4 × 20.3 × 30.5 Volume = 15551.55 cubic centimeters
Q: How do I find the volume of a cuboid with a length of 3 feet, a breadth of 2 feet, and a height of 4 feet?
To find the volume of a cuboid with a length of 3 feet, a breadth of 2 feet, and a height of 4 feet, you can use the formula:
Volume = Length × Breadth × Height Volume = 36 × 24 × 48 Volume = 34560 cubic inches
Q: Can I use the formula to find the volume of a cuboid with a length of 5 meters, a breadth of 3 meters, and a height of 2 meters?
Yes, you can use the formula to find the volume of a cuboid with a length of 5 meters, a breadth of 3 meters, and a height of 2 meters. First, use the formula:
Volume = Length × Breadth × Height Volume = 5 × 3 × 2 Volume = 30 cubic meters
Q: What is the volume of a cuboid with a length of 1 kilometer, a breadth of 0.5 kilometers, and a height of 0.2 kilometers?
To find the volume of a cuboid with a length of 1 kilometer, a breadth of 0.5 kilometers, and a height of 0.2 kilometers, you can use the formula:
Volume = Length × Breadth × Height Volume = 1000 × 500 × 200 Volume = 100000000 cubic meters
Q: Can I use the formula to find the volume of a cuboid with a length of 10 yards, a breadth of 8 yards, and a height of 12 yards?
Yes, you can use the formula to find the volume of a cuboid with a length of 10 yards, a breadth of 8 yards, and a height of 12 yards. First, convert the length, breadth, and height to the same units (e.g., feet). Then, use the formula:
Volume = Length × Breadth × Height Volume = 120 × 96 × 144 Volume = 1658880 cubic feet
Q: What is the volume of a cuboid with a length of 2 kilometers, a breadth of 1 kilometer, and a height of 0.5 kilometers?
To find the volume of a cuboid with a length of 2 kilometers, a breadth of 1 kilometer, and a height of 0.5 kilometers, you can use the formula:
Volume = Length × Breadth × Height Volume = 2000 × 1000 × 500 Volume = 1000000000 cubic meters
Q: Can I use the formula to find the volume of a cuboid with a length of 15 feet, a breadth of 12 feet, and a height of 18 feet?
Yes, you can use the formula to find the volume of a cuboid with a length of 15 feet, a breadth of 12 feet, and a height of 18 feet. First, use the formula:
Volume = Length × Breadth × Height Volume = 15 × 12 × 18 Volume = 3240 cubic feet
Q: What is the volume of a cuboid with a length of 3 kilometers, a breadth of 2 kilometers, and a height of 1 kilometer?
To find the volume of a cuboid with a length of 3 kilometers, a breadth of 2 kilometers, and a height of 1 kilometer, you can use the formula:
Volume = Length × Breadth × Height Volume = 3000 × 2000 × 1000 Volume = 6000000000 cubic meters
Q: Can I use the formula to find the volume of a cuboid with a length of 20 inches, a breadth of 16 inches, and a height of 24 inches?
Yes, you can use the formula to find the volume of a cuboid with a length of 20 inches, a breadth of 16 inches, and a height of 24 inches. First, convert the length, breadth, and height to the same units (e.g., centimeters). Then, use the formula:
Volume = Length × Breadth × Height Volume = 50.8 × 40.6 × 61.0 Volume = 12531.68 cubic centimeters
Q: What is the volume of a cuboid with a length of 4 kilometers, a breadth of 3 kilometers, and a height of 2 kilometers?
To find the volume of a cuboid with a length of 4 kilometers, a breadth of 3 kilometers, and a height of 2 kilometers, you can use the formula:
Volume = Length × Breadth × Height Volume = 4000 × 3000 × 2000 Volume = 24000000000 cubic meters
Q: Can I use the formula to find the volume of a cuboid with a length of 25 feet, a breadth of 20 feet, and a height of 30 feet?
Yes, you can use the formula to find the volume of a cuboid with a length of 25 feet, a breadth of 20 feet, and a height of 30 feet. First, use the formula:
**Volume = Length × Breadth × Height