The Volume of a Rectangular Box

RECTANGULAR BOX:

A rectangular box is a solid parallelepiped with rectangles as bases. In the rectangular solid, the length(l), width(w), and height(h) are the measure of the edges and d is the length of the diagonal. The volume of a rectangular box measures the space occupied by the box in three dimensions. And it is expressed in cubic units. If the units of measurements are in inches, then volume calculation will be in cubic inches and similarly in cubic meters, and so on.

VOLUME OF RECTANGULAR BOX: Meaning and Formula

To find out the volume of the rectangular solid, you need the length, breadth, and height of the box. The multiplication of all three measurements will give you the volume.

The formula for calculating volume:

V = Length × Width × Height

V = l × w × h

Here,

The bases of the boxes are rectangular, and the formula for the area of a rectangle is:

Area = Length × Breadth

Therefore, the volume of the box  can be expressed as:

V= Area of the base × Height

Understand with an example:

You have a wooden box in the form of a rectangular solid. The length, width, and height of the box are 10 cm, 8 cm, and 7 cm respectively. Calculate the volume of the box.

V = Length × Width × Height

V = 10 cm × 8 cm × 7 cm

V = 560\mathrm{~cm}^{3}

Points to remember: There are synonyms for width and height. The terms breadth in place of width and depth in place of height are used. Assure all measurements are the same units. The area of the opposite sides of a rectangular box is equal.

Steps to calculate the volume of the box:

1. Understand the question, draw the figure of the box and label the given measurements.
2. Write the formula for finding the volume.
3. Do the calculations.
4. Provide a conclusion statement.

Example:

1. Find the volume of the box with a rectangular base. The longest side of the base is 12 m and the width is 8 m. The box has a depth of 6 m.

Solution:

STEP 1: Draw the figure and label the measurements given.

Given,

The longest side of the base of the rectangle box = 12 m (length).

The width of the base is 8 m.

Height (Depth) is 6 m.

STEP 2: Write the formula

V = length × width × height

STEP 3: Do Calculation

V = 12 m × 8 m × 6 m

V = 576\mathrm{~m}^{3}

STEP 4: Conclusion Statement

The Volume of the rectangular box is 576\mathrm{~m}^{3}.