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Thought-Process to Discover Knowledge

Welcome to nubtrek.

Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

In the topic "mensuration", the foundation focuses on learning

 •  what is measurement standard?

 •  Absolute and Derived Standards


In this page, the formula to find circumference of a circle is introduced.



click on the content to continue..

Which of the following is a meaning for the word "circumference"?

  • enclosing boundary
  • enclosing boundary
  • drop over a net

The answer is "enclosing boundary". The word "circumference" is from root words with meaning circum-(around; about) and -ferre(carrying; bearing).

What is the term used to refer "the perimeter of a curved shape"?

  • Pronunciation : Say the answer once
    Spelling: Write the answer once

The answer is "circumference". Perimeter is used for shapes of straight lines and circumference is used for shaped of curved lines.

We have learned about measurement of objects in real-life, or a line segment of arbitrary length. Some of the learnings are:

 •  The length of an object can be an integer value in the unit of measurement. eg: `2cm`

 •  The length of an object need not be exactly an integer value in the unit of measurement. It can be given in smaller unit of length. eg: Length of a pencil is `2cm 5mm` or `=25mm` or `=2.5cm`

 •  The length of an object can be a decimal number in which the decimals do not repeat or do not end. The practical measure of the length is limited by the accuracy of the instrument used in measuring. eg: Length of a pencil is `2.512847cdots cm`.

Similarly, the circumference of a circle of `1cm` diameter is a decimal number in which the decimals do not repeat or do not end. That number is approximately `3.14cm` or `22/7 cm`.

What is the circumference of a circle of diameter `1cm`?

  • `pi cm`
  • approximately `22/7 cm`
  • approximately `3.14cm`
  • all the above
  • all the above

The answer is "all the above"

Circumference of a circle of diameter `1cm` is represented as `pi`. For a circle of diameter `d cm` or `r cm`, the circumference is `pi d ` or `2 pi r` cm.

What is the circumference of a circle of `7cm` radius?
Approximate `pi=22/7`

  • `44cm`
  • `44cm`
  • `22cm`

The answer is "`44cm`"

Circumference of a Circle: :area by equivalence Circumference `= 2 pi r` and `=pi d`

`r` is the radius of the circle

`d` is the diameter of the circle

Solved Exercise Problem:

What is the circumference of a circle of `1/pi cm` diameter?

  • `1cm`
  • `1cm`
  • `pi cm`

The answer is "`1cm`"

                            
slide-show version coming soon