Overview
Circumference of a Circle: :
Circumference and
is the radius of the circle
is the diameter of the circle
Area of a Circle :
is the radius of the 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: 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 or or 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 cm.
Similarly, the circumference of a circle of cm diameter is a decimal number in which the decimals do not repeat or do not end. That number is approximately cm or cm.
The circumference of a circle of diameter cm is
cm
=approximately cm
= approximately cm
Circumference of a circle of diameter cm is represented as . For a circle of diameter cm or radius cm, the circumference is or cm.
The circumference of a circle of cm radius is " cm"
Approximately
What is the circumference of a circle of cm diameter?
The answer is " cm"
summary
Circumference of a Circle: :
Circumference and
is the radius of the circle
is the diameter of the circle
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 times the diameter.
Similarly, the area of a circle of 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 is or .
More details and derivation of the circumference & area of circle is given in Mensuration High
example
What is the area of a circle of cm radius?
The answer is "".
Area
summary
Area of a Circle :
is the radius of the 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