Calculating the Volume of the Rectangular Base

Oct 13, 2025 by vinooalluri.com 52 views

In this article, we will delve into the world of mathematics and explore a problem that requires us to think creatively and apply our knowledge of geometry and measurement. The problem at hand is to determine how many cubes with a side length of 3 mm will fit in a rectangular base with dimensions of 9 cm x 6 cm.

Converting Units: A Crucial Step

Before we can proceed with the problem, we need to convert the units of measurement to a consistent system. In this case, we will convert the dimensions of the rectangular base from centimeters to millimeters. We know that 1 centimeter is equal to 10 millimeters, so we can convert the dimensions as follows:

9 cm = 9 x 10 mm = 90 mm
6 cm = 6 x 10 mm = 60 mm

Calculating the Volume of the Rectangular Base

Now that we have the dimensions of the rectangular base in millimeters, we can calculate its volume. The volume of a rectangular base is given by the formula:

Volume = Length x Width x Height

In this case, the length and width of the rectangular base are 90 mm and 60 mm, respectively. Since the height of the rectangular base is not specified, we will assume that it is equal to the side length of the cube, which is 3 mm.

Volume = 90 mm x 60 mm x 3 mm = 16200 cubic mm

Calculating the Volume of a Single Cube

Next, we need to calculate the volume of a single cube with a side length of 3 mm. The volume of a cube is given by the formula:

Volume = Side Length^3

In this case, the side length of the cube is 3 mm, so we can calculate its volume as follows:

Volume = 3 mm^3 = 27 cubic mm

Determining the Number of Cubes that Fit in the Rectangular Base

Now that we have the volume of the rectangular base and the volume of a single cube, we can determine how many cubes will fit in the rectangular base. We can do this by dividing the volume of the rectangular base by the volume of a single cube:

Number of Cubes = Volume of Rectangular Base / Volume of a Single Cube = 16200 cubic mm / 27 cubic mm = 600

Therefore, the correct answer is B. 600.

Conclusion

In this article, we explored a problem that required us to think creatively and apply our knowledge of geometry and measurement. We converted the units of measurement to a consistent system, calculated the volume of the rectangular base, and determined how many cubes with a side length of 3 mm will fit in the rectangular base. The correct answer is B. 600.

Additional Tips and Variations

To make the problem more challenging, you can add a height to the rectangular base and ask the student to calculate the volume of the rectangular base with the added height.
You can also ask the student to calculate the volume of the rectangular base using different units of measurement, such as inches or feet.
To make the problem more accessible, you can use a smaller side length for the cube and ask the student to calculate the volume of the rectangular base using a smaller unit of measurement.

Frequently Asked Questions

Q: What is the volume of the rectangular base? A: The volume of the rectangular base is 16200 cubic mm.
Q: What is the volume of a single cube? A: The volume of a single cube is 27 cubic mm.
Q: How many cubes will fit in the rectangular base? A: 600 cubes will fit in the rectangular base.
Frequently Asked Questions: A Comprehensive Guide =====================================================

In this article, we will continue to explore the problem of determining how many cubes with a side length of 3 mm will fit in a rectangular base with dimensions of 9 cm x 6 cm. We will answer some of the most frequently asked questions related to this problem and provide additional insights and explanations.

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

A: The formula for calculating the volume of a rectangular base is:

Volume = Length x Width x Height

Q: How do I convert centimeters to millimeters?

A: To convert centimeters to millimeters, you can multiply the number of centimeters by 10. For example, 9 cm is equal to 9 x 10 mm = 90 mm.

Q: What is the volume of a single cube?

A: The volume of a single cube is given by the formula:

Volume = Side Length^3

In this case, the side length of the cube is 3 mm, so we can calculate its volume as follows:

Volume = 3 mm^3 = 27 cubic mm

Q: How many cubes will fit in the rectangular base?

A: To determine how many cubes will fit in the rectangular base, we can divide the volume of the rectangular base by the volume of a single cube:

Number of Cubes = Volume of Rectangular Base / Volume of a Single Cube = 16200 cubic mm / 27 cubic mm = 600

Q: What if the height of the rectangular base is not equal to the side length of the cube?

A: If the height of the rectangular base is not equal to the side length of the cube, we will need to calculate the volume of the rectangular base using the correct height. For example, if the height of the rectangular base is 5 mm, we can calculate its volume as follows:

Volume = 90 mm x 60 mm x 5 mm = 27000 cubic mm

In this case, the number of cubes that will fit in the rectangular base is:

Number of Cubes = Volume of Rectangular Base / Volume of a Single Cube = 27000 cubic mm / 27 cubic mm = 1000

Q: Can I use different units of measurement to calculate the volume of the rectangular base?

A: Yes, you can use different units of measurement to calculate the volume of the rectangular base. For example, you can use inches or feet instead of millimeters or centimeters. However, you will need to convert the units of measurement to a consistent system before calculating the volume.

Q: How can I make this problem more challenging?

A: To make this problem more challenging, you can add a height to the rectangular base and ask the student to calculate the volume of the rectangular base with the added height. You can also ask the student to calculate the volume of the rectangular base using different units of measurement, such as inches or feet.

Q: How can I make this problem more accessible?

A: To make this problem more accessible, you can use a smaller side length for the cube and ask the student to calculate the volume of the rectangular base using a smaller unit of measurement. You can also provide additional support and resources to help the student understand the concept of volume and measurement.

Conclusion

In this article, we have answered some of the most frequently asked questions related to the problem of determining how many cubes with a side length of 3 mm will fit in a rectangular base with dimensions of 9 cm x 6 cm. We have provided additional insights and explanations to help students understand the concept of volume and measurement. We hope that this article has been helpful in providing a comprehensive guide to this problem.