A Rectangular Prism Is 20 Millimeters Long And 14.2 Millimeters Wide. Its Volume Is 2,556.0 Cubic Millimeters. What Is The Height Of The Rectangular Prism

by ADMIN 155 views

Introduction

In mathematics, a rectangular prism is a three-dimensional solid object with six rectangular faces. It is also known as a rectangular cuboid. The volume of a rectangular prism can be calculated using the formula: V = lwh, where V is the volume, l is the length, w is the width, and h is the height. In this article, we will use this formula to find the height of a rectangular prism given its volume, length, and width.

Formula for the Volume of a Rectangular Prism

The formula for the volume of a rectangular prism is:

V = lwh

Where:

  • V is the volume of the rectangular prism
  • l is the length of the rectangular prism
  • w is the width of the rectangular prism
  • h is the height of the rectangular prism

Given Values

We are given the following values:

  • Length (l) = 20 millimeters
  • Width (w) = 14.2 millimeters
  • Volume (V) = 2,556.0 cubic millimeters

Calculating the Height

To find the height of the rectangular prism, we can rearrange the formula for the volume to solve for h:

h = V / (lw)

Substituting the given values, we get:

h = 2,556.0 / (20 * 14.2)

Performing the Calculation

To perform the calculation, we first multiply the length and width:

20 * 14.2 = 284

Then, we divide the volume by the product of the length and width:

2,556.0 / 284 = 9

Conclusion

Therefore, the height of the rectangular prism is 9 millimeters.

Example Use Case

This problem can be used as an example in a mathematics class to teach students how to use the formula for the volume of a rectangular prism to find the height of the prism. It can also be used to demonstrate the importance of using the correct units when performing calculations.

Real-World Applications

The formula for the volume of a rectangular prism has many real-world applications, such as:

  • Calculating the volume of a box or container
  • Determining the amount of material needed to build a structure
  • Finding the height of a rectangular prism given its volume and dimensions

Tips and Tricks

  • Make sure to use the correct units when performing calculations.
  • Use the formula for the volume of a rectangular prism to find the height of the prism.
  • Check your calculations to ensure that they are correct.

Common Mistakes

  • Failing to use the correct units when performing calculations.
  • Not rearranging the formula to solve for the correct variable.
  • Not checking calculations to ensure that they are correct.

Conclusion

In conclusion, the height of a rectangular prism can be found using the formula for the volume of a rectangular prism. By rearranging the formula to solve for the height, we can calculate the height of the prism given its volume and dimensions. This problem can be used as an example in a mathematics class to teach students how to use the formula for the volume of a rectangular prism to find the height of the prism.

Introduction

In the previous article, we discussed how to find the height of a rectangular prism given its volume, length, and width. In this article, we will provide a Q&A section to help clarify any doubts and provide additional information on the topic.

Q&A

Q: What is the formula for the volume of a rectangular prism?

A: The formula for the volume of a rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.

Q: How do I find the height of a rectangular prism given its volume and dimensions?

A: To find the height of a rectangular prism, you can rearrange the formula for the volume to solve for h: h = V / (lw). Then, substitute the given values and perform the calculation.

Q: What if I have a rectangular prism with a volume of 1,000 cubic centimeters and a length of 10 centimeters? How do I find the height?

A: To find the height, you can use the formula h = V / (lw). First, convert the volume from cubic centimeters to cubic millimeters (1 cubic centimeter = 1,000,000 cubic millimeters). Then, substitute the given values and perform the calculation.

Q: Can I use the formula for the volume of a rectangular prism to find the length or width of the prism?

A: Yes, you can use the formula to find the length or width of the prism by rearranging it to solve for l or w. For example, to find the length, you can use the formula l = V / (wh).

Q: What if I have a rectangular prism with a volume of 500 cubic millimeters and a length of 5 millimeters? How do I find the width?

A: To find the width, you can use the formula w = V / (lh). Substitute the given values and perform the calculation.

Q: Can I use the formula for the volume of a rectangular prism to find the height of a prism with a non-rectangular base?

A: No, the formula for the volume of a rectangular prism is only applicable to prisms with rectangular bases. If you have a prism with a non-rectangular base, you will need to use a different formula or method to find the volume and height.

Q: What if I have a rectangular prism with a volume of 1,000 cubic millimeters and a width of 10 millimeters? How do I find the length?

A: To find the length, you can use the formula l = V / (wh). Substitute the given values and perform the calculation.

Q: Can I use the formula for the volume of a rectangular prism to find the height of a prism with a negative volume?

A: No, the formula for the volume of a rectangular prism is only applicable to prisms with non-negative volumes. If you have a prism with a negative volume, you will need to re-evaluate the problem and ensure that the volume is non-negative.

Conclusion

In conclusion, the formula for the volume of a rectangular prism is a powerful tool for finding the height of a prism given its volume and dimensions. By rearranging the formula to solve for the height, you can calculate the height of the prism. This Q&A section provides additional information and examples to help clarify any doubts and provide additional information on the topic.

Tips and Tricks

  • Make sure to use the correct units when performing calculations.
  • Use the formula for the volume of a rectangular prism to find the height of the prism.
  • Check your calculations to ensure that they are correct.

Common Mistakes

  • Failing to use the correct units when performing calculations.
  • Not rearranging the formula to solve for the correct variable.
  • Not checking calculations to ensure that they are correct.

Real-World Applications

The formula for the volume of a rectangular prism has many real-world applications, such as:

  • Calculating the volume of a box or container
  • Determining the amount of material needed to build a structure
  • Finding the height of a rectangular prism given its volume and dimensions

Example Use Case

This problem can be used as an example in a mathematics class to teach students how to use the formula for the volume of a rectangular prism to find the height of the prism. It can also be used to demonstrate the importance of using the correct units when performing calculations.