Calculating the Volume of the Rectangular Box

Oct 13, 2025 by miodeya.com 52 views

Understanding the Problem

In this problem, we are given the external length, breadth, and height of a rectangular box, which are 20 cm, 12 cm, and 6 cm respectively. We are also given the length of the wood, which is 0.5 cm. Our goal is to find the volume of the rectangular box's space.

What is Volume?

Volume is the amount of space inside a 3D object. It is measured in cubic units, such as cubic centimeters (cm³) or cubic meters (m³). To find the volume of a rectangular box, we need to multiply its length, breadth, and height.

Calculating the Volume

The formula to find the volume of a rectangular box is:

Volume = Length × Breadth × Height

In this case, the length, breadth, and height of the rectangular box are 20 cm, 12 cm, and 6 cm respectively. However, we need to subtract the length of the wood from each dimension to find the internal dimensions of the box.

Internal Dimensions

To find the internal dimensions of the box, we need to subtract the length of the wood from each dimension.

Internal Length = External Length - Length of Wood Internal Breadth = External Breadth - Length of Wood Internal Height = External Height - Length of Wood

Plugging in the values, we get:

Internal Length = 20 cm - 0.5 cm = 19.5 cm Internal Breadth = 12 cm - 0.5 cm = 11.5 cm Internal Height = 6 cm - 0.5 cm = 5.5 cm

Calculating the Volume of the Rectangular Box

Now that we have the internal dimensions of the box, we can calculate its volume using the formula:

Volume = Internal Length × Internal Breadth × Internal Height

Plugging in the values, we get:

Volume = 19.5 cm × 11.5 cm × 5.5 cm Volume = 1331.875 cm³

Conclusion

In this problem, we were given the external length, breadth, and height of a rectangular box, as well as the length of the wood. We used the formula for volume to find the volume of the rectangular box's space. We first calculated the internal dimensions of the box by subtracting the length of the wood from each dimension. Then, we used the internal dimensions to calculate the volume of the box.

Key Takeaways

The volume of a rectangular box is calculated by multiplying its length, breadth, and height.
To find the internal dimensions of a box, we need to subtract the length of the wood from each dimension.
The formula for volume is: Volume = Internal Length × Internal Breadth × Internal Height.

Real-World Applications

This problem has real-world applications in various fields, such as:

Architecture: To calculate the volume of a building or a room.
Engineering: To calculate the volume of a container or a tank.
Science: To calculate the volume of a sample or a container.

Practice Problems

A rectangular box has an external length of 15 cm, a breadth of 10 cm, and a height of 8 cm. If the length of the wood is 0.2 cm, what is the volume of the rectangular box's space?
A rectangular box has an external length of 20 cm, a breadth of 12 cm, and a height of 6 cm. If the length of the wood is 0.5 cm, what is the volume of the rectangular box's space?

Solutions

Internal Length = 15 cm - 0.2 cm = 14.8 cm Internal Breadth = 10 cm - 0.2 cm = 9.8 cm Internal Height = 8 cm - 0.2 cm = 7.8 cm Volume = 14.8 cm × 9.8 cm × 7.8 cm = 1121.904 cm³
Internal Length = 20 cm - 0.5 cm = 19.5 cm Internal Breadth = 12 cm - 0.5 cm = 11.5 cm Internal Height = 6 cm - 0.5 cm = 5.5 cm Volume = 19.5 cm × 11.5 cm × 5.5 cm = 1331.875 cm³
Frequently Asked Questions (FAQs) =====================================

Q: What is the formula to find the volume of a rectangular box?

A: The formula to find the volume of a rectangular box is: Volume = Length × Breadth × Height.

Q: How do I find the internal dimensions of a box?

A: To find the internal dimensions of a box, you need to subtract the length of the wood from each dimension. For example, if the external length is 20 cm and the length of the wood is 0.5 cm, the internal length would be 20 cm - 0.5 cm = 19.5 cm.

Q: What is the difference between external and internal dimensions?

A: External dimensions refer to the dimensions of a box from the outside, including the thickness of the wood. Internal dimensions, on the other hand, refer to the dimensions of a box from the inside, excluding the thickness of the wood.

Q: Can I use the same formula to find the volume of a cube?

A: Yes, you can use the same formula to find the volume of a cube. However, since a cube has equal dimensions, you can simply cube the length of one side to find the volume.

Q: How do I calculate the volume of a box with irregular dimensions?

A: To calculate the volume of a box with irregular dimensions, you need to break down the box into smaller rectangular boxes and calculate the volume of each one separately. Then, add up the volumes of all the smaller boxes to find the total volume of the box.

Q: What is the unit of measurement for volume?

A: The unit of measurement for volume is typically cubic units, such as cubic centimeters (cm³) or cubic meters (m³).

Q: Can I use the formula to find the volume of a box with negative dimensions?

A: No, you cannot use the formula to find the volume of a box with negative dimensions. Volume is a positive quantity, and negative dimensions do not make sense in this context.

Q: How do I round off the volume of a box to the nearest whole number?

A: To round off the volume of a box to the nearest whole number, you can use the rounding rules for decimal numbers. For example, if the volume is 12.5 cm³, you can round it off to 13 cm³.

Q: Can I use the formula to find the volume of a box with fractional dimensions?

A: Yes, you can use the formula to find the volume of a box with fractional dimensions. However, you need to make sure that the dimensions are in the correct units and that the formula is applied correctly.

Q: How do I convert the volume of a box from one unit of measurement to another?

A: To convert the volume of a box from one unit of measurement to another, you need to use the conversion factor between the two units. For example, if you want to convert the volume from cubic centimeters (cm³) to cubic meters (m³), you can use the conversion factor 1 m³ = 1,000,000 cm³.

Q: Can I use the formula to find the volume of a box with dimensions in different units?

A: No, you cannot use the formula to find the volume of a box with dimensions in different units. The formula requires that all dimensions be in the same unit of measurement.

Q: How do I calculate the volume of a box with a curved surface?

A: To calculate the volume of a box with a curved surface, you need to use the formula for the volume of a sphere or a cylinder, depending on the shape of the curved surface.

Q: Can I use the formula to find the volume of a box with a non-rectangular shape?

A: No, you cannot use the formula to find the volume of a box with a non-rectangular shape. The formula is only applicable to rectangular boxes.