Online Math Center

Measuring And Converting Lengths, Areas, And Volumes

Since people began to discover all the wonders mathematics could bring to civilization thousands of years ago, we’ve been using numbers and mathematics to identify and express various features of pretty much everything in our physical world. 


Thanks to the mathematicians that came before us, we can measure things like length, area, and volume, and express these findings in several ways.


Nowadays, most countries in the world use something called the metric system, a standardized method of measurement that is easy to understand and use. On the other hand, in some places, and for some particular reasons, other less common and more seemingly strange systems of measurement are used to find lengths, areas, and volumes of objects.


Let’s take a closer look at how we measure the length, area, and volume of various objects, so we can find out what systems are used and, importantly, how we can quickly convert our answer to express it in various ways.


Length, Area, Volume… What’s The Difference?


Length, area, and volume are three-dimensional measures of objects. Length measures one-dimensional objects, area measures two-dimensional objects, and volume measures, you guessed it, three-dimensional objects.


In geometry, we measure lines in length, we measure shapes such as circles and triangles in area, and we measure three-dimensional objects, such as pyramids, cubes, or cones. 


The number of dimensions in the shapes that we measure also gives us a hint about how we will express our answers.


One-dimensional measurements – such as length – will be expressed as normal numbers. Two-dimensional shapes will be expressed as a number squared (to the power of two), and three-dimensional shapes will be written as numbers cubed (to the power of three. 


It’s very important to always write your answers to the appropriate power when measuring length, area, and volume. 


The formulae for finding these measurements will vary from shape to shape. Some of the most commonly seen are:


Area of a square: A = side², where the side is one side of a square.


Volume of a cone: V = πr²h.


Area of a rectangle: A = L x W, where L is the length of the rectangle and W is 

the width of the rectangle.


Volume of a cube: V = a³, where a is the edge length of a cube.

Can you remember the formula for the area of a triangle, from a recent OMC blog article?

Metric Measuring

Now that we know the difference between length, area, and volume, we need to understand what the Metric System is and why it was developed in the first place.


What is important to know is that, just because length, area, and volume are established measures does not mean they are always expressed in the same way.


There are many, many ways of expressing the length of a piece of string. 


We can measure it in feet, in yards, in furlongs… the list goes on!

As you can imagine, the same is true for area and volume. Is the area of a square expressed in square feet, hectares, or acres?


Should a swimming pool be measured in quarts? 


The truth is, we can measure these objects and express them in any of the terms laid out above. 


The other truth is that, while it is great to know how to express lengths, areas, and volumes in various ways, we need a more universally-understandable system of measuring these objects.


That system is the Metric System.


It is the international standard system of measurement based on the standard decimal number system. Each quantity it measures has one unit to measure it, and subunits based on multiples and submultiples of 10. This makes calculations very straightforward. 


For the base unit length, the metric unit is meters (m). From this, we get the derived units square meter (m²) and cubic meter (m³), which we use to measure area and volume, respectively.


The different units of measurement can be tough to grasp at first glance, but in time, young math students become quick at identifying which of the quick conversion calculations needs to be done. To help them get the hang of it, here is a useful conversion calculator, to help them practice converting lengths, areas, volumes, and other measurements to a variety of units of measurement.


Keep Their Mind In Shape With OMC Math Courses

Young Math students are going to be expected to get to grips with the entire geometry curriculum – not just length, area, and volume – this school year. Give them every chance of achieving high grades by enrolling them now in an OMC 5th Grade Math Course. Better yet, for an extra edge on the competition, take a look at the options on offer in OMC 1-1 Tutoring Courses.


Contact OMC today to get your young learner on the path to reaching their mathematic potential.

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