Measurement

The word “measurement” is derived from the Greek word "metron," which means a limited proportion. This word also finds its roots in the words "moon" and "month," possibly because astronomical objects were among the first methods to measure time.

Table of Content

Introduction to Measurement

Measurement refers to the comparison of an unknown quantity with a known quantity. The result of the measurement is a numeric value with certain units. We can measure the length, weight, and capacity (volume) of any given object. Let us:

  • learn how to measure the area and perimeter of plane shapes.
  • explore solid shapes and learn how to measure their surface areas and volumes.
  • know about reading the clock and the calendar.

You can go ahead and explore all important topics in Measurement by selecting the topics from this list below:

Metric System Surface Area
Perimeter Volume
Area Time
Solid Shapes Unit Conversion

Measurement involves measuring or quantifying the length, weight, and capacity of something. There are two main "Systems of Measurement": Metric and US Standard. The table given below summarizes the frequently used units of measurement for length, weight, and capacity in both the Systems of Measurement.

metric-conversions

Measurements are made by comparing a quantity with a standard unit. In this section, you will learn about measuring length, measuring weight, and measuring capacity.

Measurement of 2-D Shapes

square is a 2D shape whereas a cube is a 3D shape. 2Dshapes, as the name suggests, have only two of these measurements. A two-dimensional shape does not have any depth.

Since 2-D shapes only have two dimensions, their measurement can be done in two ways, we can either calculate the area they occupy or the perimeter(that is, the length of their boundary.

Perimeter

The total length of the boundary of a closed two-dimensional shape is called its perimeter.

Example:

Perimeter-of-a-2-D-Shape

The perimeter of the figure ABCDEFA = AB + BC + CD + DE + EF + FA = (4 + 3) + 6 + 4 + 2 + 3 + (6 - 2) = 26 inches

[AB = CD + EF; FA = BC - DE] 

We now know that perimeter is the length of the boundary of a 2-dimensional figure. Let us now understand how to determine the perimeter of a triangle, perimeter of a quadrilateral, and perimeter of a circle.

Area

Area is the space occupied by a two-dimensional shape or figure.

Example:

calculating the area of mutliple figures given

If the area of 1 square = 1 square unit, then

  • Area of shape A = 1 square unit
  • Area of shape B = (1 + 1) = 2 square units
  • Area of shape C = (1 + 1 + 1) = 3 square units
  • Area of shape D = (0.5 + 1 + 0.5) = 2 square units

Now that you know what an area is, let's learn how to find the area of a triangle, area of a quadrilateral, and area of a circle.

Measurement of Solid Shapes

Solid figures are three-dimensional objects. They have a width, a depth, and a height.

Example:

Measurement of Solid Shape

We already know solid shapes are three-dimensional. These 3D objects occupy some space. We will be studying some of the topics like cuboid basics, right circular cylinder basics, right circular cone basics, and sphere basics.

Surface Area

The surface area of a solid shape is the combined area of all its faces. Thus, the surface area of a solid shape with flat faces is the combined area of all its faces.

Example:

Surface-Area-of-Cube

In this topic of Surface Area, you will learn how to determine the surface area of a cuboid, surface area of cylinder, surface area of cone, surface area of sphere, and surface area of rectangular prism.

Volume

Volume is the space enclosed or occupied by any three-dimensional object or solid shape.

Example:

Measuring Volume

Initial volume of water in the container = 20 units, Volume of water when the object is placed inside the container = 30 units. Therefore, the volume of the object = 30 - 20 = 10 units

Finding the volume of an object can help us determine the amount required to fill that object. For example, the amount of water in a bottle. We will now learn how to find the volume of a cuboid, volume of a cylinder, volume of a cone, volume of a sphere, and volume of a pyramid.

Time Measurement

Time is the ongoing sequence of events taking place. It is used to quantify the duration of the events. It also helps us set the start time or the end time of events.

Example:

AM and PM

The relation between different units of time measurement can be sen in the figure below:

Time Measurement

  • 1 year = 12 months = 365/366 days
  • 1 month = 4 weeks = 30/31 days
  • 1 week = 7 days
  • 1 day = 24 hours
  • 1 hour = 60 minutes
  • 1 minute = 60 seconds

One of the very first experiences we have with mathematics is learning how to measure Time. You may already know that the measurement of time is done using a watch and a calendar. Now, let's learn how to read and represent time along with how to read a calendar.


FAQs on Measurement

What are the 7 Basic Units of Measurement?

The seven SI base units are:

  • Length - meter (m)
  • Time - second (s)
  • Amount of substance - mole (mole)
  • Electric current - ampere (A)
  • Temperature - kelvin (K)
  • Luminous intensity - candela (cd)
  • Mass - kilogram (kg)

What is the Formula for Surface Area?

The surface area of a solid shape is the combined area of all its faces. Thus, 

  • Surface Area of Cuboid = 2(lh + lb + bh)
  • Surface Area of Cube = 6s
  • Surface Area of Cone = π r(r + s)
  • Surface Area of Cylinder = 2πr (r+h)
  • Surface Area of Sphere =  4πr2

What is an Area Formula?

The most basic formula to find the area of a 2-D shape is the formula for the area of a rectangle. That is, the area of the rectangle is the length multiplied by the width. Also, as a special case, where l = w, that is the case of a square, then the formula for the area of a square with side length s is A = s2 (square).

What System of Measurement is used in the US?

The United States has introduced its own customary units which are extensively used in various fields which is USCS. The units they use for measurement include feet, inches, pounds, ounces, etc. 

Why is Measurement Important?

It is important to measure certain things to understand the world around us, such as distance, time, and accuracy, and all. Measurement is a concept that is used in almost all fields, a few of them are given below.

  • Measurement of agricultural fields, floor areas required for purchase/selling transactions.

  • Measurement of volumes required for packaging milk, liquids, solid edible food items.

  • Measurements of surface areas required for estimation of painting houses, buildings etc.

What is the Main System of Measurement?

The main system of measurement is the international system of units(SI) units, and all other systems of measurement is linked to it. The British Imperial system and the US customary system linked to the SI units of measurement with the units of conversion, and can be conveniently used to convert from one unit to another.

Why is it Important to Measure Time?

Time is a very important measurement that helps us fix the duration or length of any event, specify when an event will start and end, and also compare the duration of any two events.


Solved Examples on Measurement

Example 1: The dimensions of a rectangular park are 15 yards and 8 yards. Find its area.

Solution: 

The area of a rectangle is the product of its length and breadth. Therefore, Area = 15×8=120 yard2

Example 2: Find the measurement of time between 2:00 to 4:00.

Solution: 

There are 2 hours between 2:00 and 4:00. Therefore, the time between 2:00 and 4:00 is 2 hours.

Practice Questions on Measurement

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

 
 
 
 
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