[Maths Class Notes] on Relation Between Inch and cm Pdf for Exam

1 Meter to centimeter is the base unit of length and distance in the International System of Units (SI).

 1m = 100cm

A centimeter is a unit of length in the International System of Units (SI), the current form of the metric system. 

1cm = 1/100m

Foot in cm

A foot is a non-SI unit of distance or length, measuring around a third of a meter. One yard consists of three feet, and twelve inches make a foot.

1 foot = 30.48 cm

A centimeter is a unit of length that is equal to one-hundredth of a meter. 

1 cm = 0.0328084 foot

cm to Inches to Feet 

1cm =  0.0328 feet or 0.3937 inches

The relation between inch and centimeter (cm) is one of the most used calculations in our daily life. But to understand the relation between inch and centimeter (cm), one has to know the definition of inch and centimeter (cm). 

Both inch and centimeter (cm) are the systems used to measure sets of length, weight, capacity temperature, speed, etc. 

Conversion of Units

In Mathematics, the conversion is one of the most important parts while solving problems with a different system of measurement to carry out the required calculations.  

For example: In a question, you are asked to find the perimeter of a rectangle in inches, but the breadth given is in meters and the height in centimeters (cm). First, you have to convert meter (m) in centimeter (cm) then solve the perimeter when you find the value of perimeter, and you have to change the answer into inches using the relation between centimeter (cm) and inch. Conversion of units is very easy, but it tends to be confusing because of the operation of numbers to multiply and divide. 

Why and How to Convert Units? 

We need to convert units depending on the situation. For example height of a person is measured in centimeter (cm), while distance covered by a vehicle in kilometer (km), thickness of stainless steel in millimeter (mm) distance between two ends of a room in meter (m), biceps, and chest in inches.

Thus, to convert any of these units, we have to understand the concept of the relation between those units.

So, in this article, we are going to understand the relation between inches and centimeters (cm). 

Inch

Inch is a system used to measure quantities like length, weight, capacity, temperature, etc. based on the English system of measurement. Inch is defined as the unit of measurement of length denoted by ‘in’ and represented by the symbol ‘ ” ‘. Two half inches or four-quarter inches are combined to form one whole of an inch.

For example, 10 inches can be written as ‘4 in’ or represented by ‘4″ ‘. 

Representation of Inch

1″ = One-inch

½” = One half of an inch

¼” = One-quarter of an inch

⅛” = One-eighth of an inch

1/16″ = One-sixteenth of an inch

Centimeter (cm)

Centimeter is used to measure the length in the metric system. Centimeter is 1/100th of a meter which means 

1 meter (m) = 100 centimeter (cm)  

or 

1 centimeter (cm) = 0.01 meter (m)

and 1 centimeter (cm) is also equal to 10 millimeter (mm).

‘CM’ is abbreviated at the place of ‘centimeter ‘. Also when 1 centimeter (cm) is converted into inches or is equal to 0.3937 inches. 

Conversion from Centimeter (cm) to Inches

Questions:

Question 1.  Convert 12 cm into inches. 

Ans: To convert 12 cm to inches, we need to divide the amount by 2.54.                

12 ÷ 2.54 = 4.724 (to 3dp)

So, 12 cm = 4.724 inches.

Question 2. A three feet tall person is 36 inches tall. Calculate how many centimeters tall a three feet person.

Ans: We know that, 36 in = 36 in (2.54 cm/ 1 in)     

Now cancel out inches, We get  36 in = 36 x 2.54

36 in = 91.44 cm

Therefore, a three feet person is 91.44 centimeters tall.

Question 3.  Given figure depicts an archery target marked with its five scoring areas from the center outwards as Yellow, Orange, Purple, Brown, and Grey. The diameter of the region representing Yellow score is 21 cm, and each of the other bands is 10.5 cm wide then find the area of each of the five scoring regions. 

Ans:   Diametre of yellow circle = 21cm          

So, Radius of yellow = Diametre/2 = 21/2 cm = 10.5 cm            

Now,  Area of yellow = πrGOLD2  = 22/7 ×10.5 × 10.5      =   346.5 cm2   

Now,  Radius of orange = Radius of yellow + width of band  

= 10.5 + 10.5   

=  21 cm     

Area of (orange + yellow) =  πrRED2  

=  22/7 × 21 × 21

=   1386 cm2      

Area of orange = Area of (orange + yellow) – Area of yellow

= 1386 – 346.5    

= 1039.5 cm     

Radius of purple = Radius of orange + Width of band

= 21 + 10.5  

= 31.5 cm    

Area of (yellow + orange + purple) = πr2 

= 22/7 × (31.5)2    

= 22/7 × 31.5 × 31.5 

= 22/7 × 4.5 × 31.5

= 3118.5 cm2      

Area of purp
le = Area of (orange + yellow + purple) – Area of (orange + yellow)                          = 3118.5 – 1386  

 = 1732.5 cm2    

Radius of brown = Radius of purple + Width of band 

=  31.5 + 10.5     

=  42 cm    

Area of (yellow + orange + purple + brown) = πr2  

=   22/7 × (42)2 

=   22/7 × 42 × 42 

=   5544 cm     

Area of brown portion =  Area of (yellow + orange + purple + brown) – Area of (yellow + orange + purple)     

=   5544 – 3118.5 

=   2425.5 cm2    

Radius of grey = Radius of brown + width of band

=   42 + 10.5 

=    52.5 cm2   

Area of grey portion = Area of (yellow + orange + purple + brown + grey) – Area of (yellow + orange + purple + brown)

=   8662.5 – 5544 

= 3118.5 cm2 

Measurement Units

Measurement is the quantification of characteristics of an object that can help to compare the given object with other objects. This helps in measuring physical quantities. The subject of measurement is useful in the field of metrology.

There are usually four units of measurement to choose from, millimeter, centimeter, inch, and foot. A meter stick is used for measuring small distances. For small distances, the metric unit meter and yard are used. Systems of measurement include the international system of units SI.

Units of Measurement are based on 

1. Measurement of Length 

The base unit of length is meter.

We measure smaller objects using a smaller unit which is centimeter and longer distances using a bigger unit which is kilometers. Millimeter (mm) Centimeter (CM) Meter( m ) and kilometer (km) are the common units of measuring length.

The below table shows the measurement of length.

1 Km=1000m                          1M=100cm                        1cm=10mm

Mm is the Smallest unit of length

2. Measurement of Weight

The basic unit of Weight is gram. The weight of rice, sugar, vegetables is expressed in g mg, kg. The weight of smaller objects such as a Matchbox is expressed in MG. The vegetable and fruit vendors use the beam balance of weighing balance.  Nowadays electronic weighing machines are also quite popular in supermarkets and bigger stores

1 Kg=1000g

1g=1000mg

3. Measurement of Capacity

We compute the amount of liquid in a container by measuring its volume. The basic unit of capacity is liter kilo l and l are used to measure large amounts of liquid whereas an ml is used to measure small amounts of liquids.

1 Kl=1000 l

1 l=1000 ml

Importance of Measurement

The action of measuring anything, or a certain number of objects, is a measurement. Also measuring certain things correctly is very necessary including distance, time, and accuracy. We can really know the universe around us by measuring such occurrences or, in other words, by taking such measurements. Measurements are not only applicable in physics and Math but they go handy for students too.

It gives students a clear understanding of the role of assessment in the industrial processes such as proper evaluation of assessments and standardized tests and how to use the given data in their daily lives. Students have a right to know the progress they are making whether they have obtained the objective or not thus they must know the results. It will help them to study and work hard.