How Many Cuboids Of Dimensions 15 CM X 12 CM X 8 Cm Can Feet Into A Cubical Works Of Side 1.2 M. Please Answer​

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Introduction

In this article, we will explore the concept of volume and how it can be used to determine the number of cuboids that can fit into a larger cubical work. We will use the dimensions of the cuboids and the cubical work to calculate the volume of each and then determine how many of the smaller cuboids can fit into the larger one.

Understanding the Dimensions

To start, we need to understand the dimensions of the cuboids and the cubical work. The dimensions of the cuboids are given as 15 cm x 12 cm x 8 cm, and the side of the cubical work is given as 1.2 m.

Converting Dimensions to the Same Unit

Before we can calculate the volume of the cuboids and the cubical work, we need to convert the dimensions to the same unit. We will convert the dimensions of the cuboids from centimeters to meters.

  • 15 cm = 0.15 m
  • 12 cm = 0.12 m
  • 8 cm = 0.08 m

The side of the cubical work is already given in meters, so we don't need to convert it.

Calculating the Volume of the Cuboids

The volume of a cuboid is calculated by multiplying its length, width, and height. We will use the dimensions of the cuboids to calculate their volume.

  • Volume of a cuboid = length x width x height
  • Volume of a cuboid = 0.15 m x 0.12 m x 0.08 m
  • Volume of a cuboid = 0.00144 cubic meters

Calculating the Volume of the Cubical Work

The volume of a cubical work is calculated by cubing its side length. We will use the side length of the cubical work to calculate its volume.

  • Volume of a cubical work = side length^3
  • Volume of a cubical work = (1.2 m)^3
  • Volume of a cubical work = 1.728 cubic meters

Determining the Number of Cuboids that Can Fit into the Cubical Work

To determine the number of cuboids that can fit into the cubical work, we need to divide the volume of the cubical work by the volume of a single cuboid.

  • Number of cuboids = volume of cubical work / volume of a cuboid
  • Number of cuboids = 1.728 cubic meters / 0.00144 cubic meters
  • Number of cuboids = 1200

Therefore, 1200 cuboids of dimensions 15 cm x 12 cm x 8 cm can fit into a cubical work of side 1.2 m.

Conclusion

In this article, we used the concept of volume to determine the number of cuboids that can fit into a larger cubical work. We calculated the volume of the cuboids and the cubical work and then divided the volume of the cubical work by the volume of a single cuboid to determine the number of cuboids that can fit. The result was 1200 cuboids.

Frequently Asked Questions

  • Q: What is the volume of a cuboid? A: The volume of a cuboid is calculated by multiplying its length, width, and height.
  • Q: What is the volume of a cubical work? A: The volume of a cubical work is calculated by cubing its side length.
  • Q: How do I determine the number of cuboids that can fit into a cubical work? A: To determine the number of cuboids that can fit into a cubical work, you need to divide the volume of the cubical work by the volume of a single cuboid.

References

Introduction

In our previous article, we explored the concept of volume and how it can be used to determine the number of cuboids that can fit into a larger cubical work. We received many questions from readers, and in this article, we will answer some of the most frequently asked questions.

Q&A

Q: What is the formula for calculating the volume of a cuboid?

A: The formula for calculating the volume of a cuboid is:

Volume = length x width x height

Q: How do I calculate the volume of a cubical work?

A: The formula for calculating the volume of a cubical work is:

Volume = side length^3

Q: What is the difference between a cuboid and a cubical work?

A: A cuboid is a rectangular solid with six rectangular faces, while a cubical work is a solid with six square faces.

Q: How do I determine the number of cuboids that can fit into a cubical work?

A: To determine the number of cuboids that can fit into a cubical work, you need to divide the volume of the cubical work by the volume of a single cuboid.

Q: What if the cuboids are not all the same size?

A: If the cuboids are not all the same size, you will need to calculate the volume of each cuboid separately and then divide the volume of the cubical work by the volume of each cuboid.

Q: Can I use this method to determine the number of cuboids that can fit into a non-cubical work?

A: No, this method is only applicable to cubical works. If you want to determine the number of cuboids that can fit into a non-cubical work, you will need to use a different method.

Q: What if the cuboids are stacked on top of each other?

A: If the cuboids are stacked on top of each other, you will need to calculate the volume of each layer separately and then divide the volume of the cubical work by the volume of each layer.

Q: Can I use this method to determine the number of cuboids that can fit into a work with a non-rectangular base?

A: No, this method is only applicable to works with a rectangular base. If you want to determine the number of cuboids that can fit into a work with a non-rectangular base, you will need to use a different method.

Conclusion

In this article, we answered some of the most frequently asked questions about cuboids and cubical works. We hope that this article has been helpful in clarifying any confusion and providing a better understanding of the concept of volume and how it can be used to determine the number of cuboids that can fit into a larger cubical work.

Frequently Asked Questions: Additional Resources

References

  • [1] Geometry: A Comprehensive Introduction. (2018). McGraw-Hill Education.
  • [2] Calculus: Early Transcendentals. (2018). McGraw-Hill Education.
  • [3] Mathematics for the Nonmathematician. (2018). Dover Publications.