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Circumference and Area of a Circle


    what you'll learn...

Overview

Circumference of a Circle: :
Circumference =2πr and =πd

r is the radius of the circle

d is the diameter of the circle circumference by equivalence Area of a Circle :
=πr2

r is the radius of the circle area of a circle

measuring arbitrary length

The word "circumference" means: enclosing boundary.

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

We 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: 2 cm

 •  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 2cm5mm or =25mm or =2.5 cm

 •  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 2.512847 cm.

Similarly, the circumference of a circle of 1 cm diameter is a decimal number in which the decimals do not repeat or do not end. That number is approximately 3.14 cm or 227 cm. circumference by equivalence The circumference of a circle of diameter 1 cm is
π cm
=approximately 227 cm
= approximately 3.14 cm

Circumference of a circle of diameter 1 cm is represented as π. For a circle of diameter d cm or radius r cm, the circumference is πd or 2πr cm.

The circumference of a circle of 7 cm radius is "44 cm"
Approximately π=227

What is the circumference of a circle of 1π cm diameter?
The answer is "1 cm"

summary

Circumference of a Circle: :
Circumference =2πr and =πd

r is the radius of the circle

d is the diameter of the circle circumference by equivalence

area is another number

We have learned the following

 •  Length of a real-life object or a line can be a decimal number in which the decimals do not end or do not repeat.

 •  Circumference of a circle is π times the diameter.

Similarly, the area of a circle of 1 cm radius is also a decimal number in which the decimals do not end or repeat. It is calculated that the area of a circle or radius r is π×r×r or =πr2.

More details and derivation of the circumference & area of circle is given in Mensuration High

example

What is the area of a circle of 1π cm radius?
The answer is "1πcm2".

Area

=πr2

=π×1π×1π

=1πcm2

summary

Area of a Circle :
=πr2

r is the radius of the circle area of a circle

Outline

The outline of material to learn "Mensuration basics : Length, Area, & Volume" is as follows.

Note: click here for detailed outline of Mensuration (Basics).

•  Measuring Basics

  →   Introduction to Standards

  →   Measuring Length

  →   Accurate & Approximate Meaures

  →   Measuring Area

  →   Measuring Volume

  →   Conversion between Units of Measure

•  2D shapes

  →   Perimeter of Polygons

  →   Area of Square & rectangle

  →   Area of Triangle

  →   Area of Polygons

  →   Perimeter and area of a Circle

  →   Perimeter & Area of Quadrilaterals

•  3D shapes

  →   Surface Area of Cube, Cuboid, Cylinder

  →   Volume of Cube, Cuboid, Cylinder