Calculate The Volume Of A Rectangular Prism With Length 5 Cm, Width 5 Cm, And Height 20 Cm, Rounded To The Nearest Tenth Of A Cubic Centimeter.

by ADMIN 144 views

In the realm of geometry, understanding how to calculate the volume of three-dimensional shapes is a fundamental skill. Among these shapes, the rectangular prism stands out as one of the most common and readily encountered in our daily lives. From boxes and bricks to buildings and rooms, rectangular prisms surround us, making the ability to determine their volume a valuable asset. This comprehensive guide will walk you through the process of calculating the volume of a rectangular prism, providing a clear, step-by-step approach that will empower you to confidently tackle such calculations.

Understanding Rectangular Prisms

Before diving into the calculation itself, let's first establish a clear understanding of what a rectangular prism is. A rectangular prism is a three-dimensional geometric shape characterized by six faces, all of which are rectangles. These faces meet at right angles, forming a box-like structure. Think of a classic shoebox or a brick – these are excellent examples of rectangular prisms. To fully define a rectangular prism, we need to consider its three key dimensions: length, width, and height.

  • Length: The length is the longest dimension of the rectangular base of the prism. It's the distance along the longest side of the rectangular face.
  • Width: The width is the shorter dimension of the rectangular base of the prism. It's the distance along the shorter side of the rectangular face.
  • Height: The height is the vertical distance from the base to the top face of the prism. It represents the prism's extension in the third dimension.

These three dimensions – length, width, and height – are the building blocks for calculating the volume of a rectangular prism.

The Formula for Volume

The volume of a three-dimensional shape represents the amount of space it occupies. For a rectangular prism, the volume is calculated using a straightforward formula that incorporates its length, width, and height. The formula is:

Volume = Length × Width × Height

This formula expresses the fundamental relationship between the dimensions of a rectangular prism and its capacity. To find the volume, simply multiply the length, width, and height together. The result will be the volume, expressed in cubic units (e.g., cubic centimeters, cubic meters, cubic inches).

Step-by-Step Calculation

Now, let's break down the calculation process into a series of clear steps:

  1. Identify the Dimensions: The first step is to identify the length, width, and height of the rectangular prism. These dimensions will typically be provided in the problem statement or can be measured directly if you have a physical prism.
  2. Write Down the Formula: Write down the formula for the volume of a rectangular prism: Volume = Length × Width × Height. This will serve as a visual reminder of the calculation you need to perform.
  3. Substitute the Values: Substitute the numerical values of the length, width, and height into the formula. Replace the variables (Length, Width, Height) with their corresponding measurements.
  4. Multiply the Values: Perform the multiplication operation. Multiply the length, width, and height together. Make sure to pay attention to the units of measurement and maintain consistency throughout the calculation.
  5. State the Answer with Units: Once you've obtained the numerical result, state the answer along with the appropriate cubic units. For example, if the length, width, and height are given in centimeters, the volume will be expressed in cubic centimeters (cm³).

Example Calculation

Let's illustrate the calculation process with an example. Suppose we have a rectangular prism with the following dimensions:

  • Length = 5 cm
  • Width = 5 cm
  • Height = 20 cm

Following the steps outlined above:

  1. Identify the Dimensions: We have already identified the dimensions: Length = 5 cm, Width = 5 cm, Height = 20 cm.
  2. Write Down the Formula: Volume = Length × Width × Height
  3. Substitute the Values: Volume = 5 cm × 5 cm × 20 cm
  4. Multiply the Values: Volume = 500 cm³
  5. State the Answer with Units: The volume of the rectangular prism is 500 cubic centimeters.

Rounding to the Nearest Tenth

In some cases, you may be asked to round the calculated volume to a specific decimal place, such as the nearest tenth. Rounding is a process of approximating a number to a desired level of precision. To round to the nearest tenth, follow these steps:

  1. Identify the Tenths Place: Locate the digit in the tenths place (the first digit after the decimal point).
  2. Look at the Next Digit: Examine the digit immediately to the right of the tenths place (the hundredths place).
  3. Rounding Rule:
    • If the digit in the hundredths place is 5 or greater, round the digit in the tenths place up by 1.
    • If the digit in the hundredths place is less than 5, leave the digit in the tenths place as it is.
  4. Drop the Remaining Digits: Remove all digits to the right of the tenths place.

For example, if we calculated a volume of 500.47 cm³ and needed to round to the nearest tenth, we would follow these steps:

  1. Identify the Tenths Place: The digit in the tenths place is 4.
  2. Look at the Next Digit: The digit in the hundredths place is 7.
  3. Rounding Rule: Since 7 is greater than 5, we round the 4 in the tenths place up to 5.
  4. Drop the Remaining Digits: We drop the 7 in the hundredths place.

The volume rounded to the nearest tenth is 500.5 cm³.

Practical Applications

The ability to calculate the volume of rectangular prisms has numerous practical applications in everyday life and various professional fields. Here are a few examples:

  • Construction: Calculating the volume of concrete needed for a foundation or the amount of material required to build a wall.
  • Packaging: Determining the size of a box or container needed to hold a specific product.
  • Interior Design: Estimating the amount of paint required to cover the walls of a room or the volume of storage space in a cabinet.
  • Logistics: Calculating the capacity of a truck or container for shipping goods.
  • Science and Engineering: Determining the volume of liquids or solids in experiments and calculations.

Mastering the Concept

Calculating the volume of a rectangular prism is a fundamental skill that can be applied in a wide range of situations. By understanding the formula and following the step-by-step process, you can confidently determine the volume of any rectangular prism. Remember to pay attention to the units of measurement and practice rounding to the desired level of precision. With consistent practice, you'll master this concept and be well-equipped to tackle more complex geometric problems.

Real-World Examples and Problem-Solving

To further solidify your understanding, let's explore some real-world examples and problem-solving scenarios. These examples will demonstrate how the concept of rectangular prism volume applies to various situations, enhancing your ability to utilize this knowledge effectively.

Example 1: Packing a Box

Imagine you're moving and need to pack your belongings into boxes. You have a box with the following dimensions:

  • Length = 60 cm
  • Width = 40 cm
  • Height = 30 cm

You want to know the maximum volume of items you can fit into the box. To find this, you need to calculate the volume of the box.

Using the formula Volume = Length × Width × Height:

Volume = 60 cm × 40 cm × 30 cm = 72,000 cm³

Therefore, the box can hold up to 72,000 cubic centimeters of items. This knowledge helps you estimate how many items you can pack into the box and plan your packing strategy accordingly.

Example 2: Building a Fish Tank

You're planning to build a rectangular fish tank for your new aquatic pets. You want the tank to have the following dimensions:

  • Length = 80 cm
  • Width = 35 cm
  • Height = 45 cm

To determine how much water the tank can hold, you need to calculate its volume.

Applying the formula Volume = Length × Width × Height:

Volume = 80 cm × 35 cm × 45 cm = 126,000 cm³

Since 1 cubic centimeter is equivalent to 1 milliliter, the tank can hold 126,000 milliliters or 126 liters of water. This calculation is crucial for selecting the appropriate filter, heater, and other equipment for your fish tank.

Example 3: Calculating Room Capacity

Consider a rectangular room in your house with the following dimensions:

  • Length = 5 meters
  • Width = 4 meters
  • Height = 2.5 meters

You want to determine the total volume of air in the room, which can be useful for calculating heating or cooling requirements.

Using the formula Volume = Length × Width × Height:

Volume = 5 m × 4 m × 2.5 m = 50 m³

The room has a volume of 50 cubic meters. This information can help you choose the right size air conditioner or heater for the room, ensuring optimal comfort and energy efficiency.

Problem-Solving Strategies

When faced with problems involving the volume of rectangular prisms, consider these strategies:

  1. Visualize the Problem: Draw a diagram of the rectangular prism, labeling the dimensions. This visual representation can aid your understanding and problem-solving process.
  2. Identify Knowns and Unknowns: Clearly identify the given dimensions (length, width, height) and what you need to find (volume). This step helps you focus on the relevant information.
  3. Apply the Formula: Use the formula Volume = Length × Width × Height to calculate the volume. Ensure you substitute the correct values for each dimension.
  4. Check Units: Pay close attention to the units of measurement. Ensure all dimensions are in the same units before performing the calculation. If necessary, convert units to maintain consistency.
  5. Round Appropriately: If the problem requires rounding, follow the rounding rules to round the answer to the specified decimal place.
  6. Interpret the Result: Consider the practical meaning of the calculated volume in the context of the problem. Does the answer make sense? Can you use the result for further calculations or decision-making?

By mastering these problem-solving strategies, you'll be well-prepared to tackle a wide variety of real-world problems involving the volume of rectangular prisms.

Conclusion

Calculating the volume of a rectangular prism is a fundamental skill with numerous applications in daily life and various professions. By understanding the formula, following the step-by-step process, and practicing with real-world examples, you can confidently master this concept. From packing boxes and building fish tanks to calculating room capacity and solving complex engineering problems, the ability to determine the volume of rectangular prisms empowers you to tackle a wide range of challenges. So, embrace the power of geometry, and let your knowledge of rectangular prism volume guide you towards success!