Packing Efficiency of a Rectangle

Most of the objects around us are 3-D objects, and the same is true for mathematical figures. Take textbooks, Macbooks, or a simple smartphone, for example, all these are 3-D objects, a 3-D rectangle or cuboid to be more specific. All these have a length, a breadth, and a height.

Proceeding further in this very context, we come across the question of how much space is encompassed within the three dimensions of these rectangles, and that is particularly the extent of the volume of that rectangle.

Using this principle, you can find the solution to simple ethical problems like the number of pages within a book, water contained within a tank, the rate of water flow in a river, and such.

The Volume of A Rectangle

is the measure of the space that is contained within that particular rectangle. The specific measurement of the volume of a rectangle determines the extent of another object or matter utilizing which the space inside the rectangle can be completely occupied.

The measure of the volume of a rectangle is given by the product of the three dimensions of the rectangle.

The volume of a rectangle = Length x Breadth x Height

Step to Step Guide to Find the Volume of a Rectangle

By following the below-mentioned steps, you can accurately calculate the volume of a rectangle rather conveniently and effectively:

1. Measure of Dimensions

Talking of the concept of the volume or space contained within a figure, it is the basic requirement for the figure to have at least a minimum of here dimensions. And, in the case of the 3-D rectangle (or Cuboid), there are exactly three dimensions. To calculate the volume of a rectangle, these three dimensions, namely length, breadth, and height, are essentially needed.

The fact is to be kept in regard that the measure of any dimension of a rectangle can never be a negative number. The dimensions of a rectangle are always a positive number. Otherwise, the entire formulation will be theory-based, with no mathematical authorization and no relative significance.

2. Calculation Using Formula

Apply scalar multiplication over the dimensions that belong to that specific rectangle, and that operation will give the volume of the rectangle. The scalar multiplication is the same as applying the basic multiplicative operations on the obtained dimensions.

i.e., If 4 units, 5 units, and 7 units are the dimensions of a rectangle, then the volume of the rectangle will be given as.

               Volume = Length x Breadth x Height = 4 x 5 x 7 = 140 units

3. Units of The Volume of A Rectangle

Similar to the volume that is a result of the product of the three dimensions of a rectangle, the finalized unit of the volume of the rectangle will be the product of the units of the dimensions of the said rectangle. The unit of a rectangle is generally given as a “unit cube”.

i.e., If 4 cm, 5 cm, and 7 cm are the dimensions of a rectangle, then the volume of the rectangle will be given as.

               Volume = Length x Breadth x Height = 4 cm x 5 cm x 7 cm = 140cm^3 = 140 cubic cm.

The Relation between the dimensions of a Rectangle and the Volume

The three dimensions of the rectangle, length, breadth, ad height, and the volume of that particular rectangle, if any three of the four quantities are known to us, it is possible for us to calculate the fourth quantity rather easily.

This particular kind of problem can be solved easily by using solutions in the form of linear equations with only one variable. The formula of the relationship between volume and dimensions will be used to calculate any one of the four entities.

               Volume = Length x Breadth x Height

Packing Efficiency

for a rectangle is the ratio of the space inside the rectangle that has already been brought into use to the total volume of the specified rectangle.

Packing efficiency is the concept regarding a 3-D figure that is brought into effect when considering the filling up of the insides or the inner space that is unoccupied within a figure.

Packing efficiency for a rectangle will give the measure of a substance that can be used to fill up a rectangle with another substance or body to a certain degree.

Types of Problems Asked Based on Concept

1. Calculating the volume of a rectangle when its dimensions are given
2. Finding the volume when there is a pre-instated stationary relation between the three dimensions.
3. Finding one dimension of the rectangle when the volume and the other two dimensions are known.
4. Finding the number of small bodies that will fill a rectangle of known dimensions.
5. The unutilized space within the rectangle after filling it up with another body.

An Example Affiliated with Each Type of Problem is As Follows:

1. If 5 cm, 10 cm, and 6 cm are the length, breadth, and height of a rectangle respectively, calculate its volume.

Volume = Length x Breadth x Height = 5 cm x 10 cm x 6 cm = 300cm^3

2. The volume of a rectangle is 600cm^2. If the two dimensions of the rectangle are 10cm and 6cm, find the third one.

Volume = Length x Breadth x Height

600cm^3 = 10cm x 6cm x Height

Height = 600/60 = 10cm

3. How many bricks of dimensions 5cm, 10cm, and 15cm will it take to completely fill up a rectangle of dimensions 10cm, 20cm, and 30cm?

The volume of the big rectangle = Length x Breadth x Height = 10cm x 20cm x 30cm = 6000cm^3

The volume of a brick = Length x Breadth x Height = 5cm x 10cm x 15cm = 750cm^3

Number of bricks it will take = the total volume of the rectangle / the volume of a brick = 6000/750 = 8

Also read: How to Find Circumference of A Circle and What is The Circumference Formula?