The “Area” of Your Circle: Determining Circumference and Area

The area of a circle: The area of the circle is how much surface area there will be inside that circular shape.

How to find the area of the circle?

The area of a circle is equal to Pi (3.14) times the radius squared, squared means multiplied by itself. Area of Circle = 3.14 X Radius X Radius.

Example: If your radius was 4 inches then your area would be 3.14 X 4 X 4 = 50.24 square inches

The circumference of the circle: The circumference of a circle is the distance around the edge of a circular shape.

How to find the circumference of a circle?

One can find circumference by multiplying pi (3.14) with diameter, the straight line passing through the center, and touching the circle at two points. The formula for finding the circumference of circles is Circumference = Pi * Diameter Example: If your diameter was 5 inches, then your circumference would be Pi X 5 = 3.14 X 5 = 15.70 inches

Circumference and area of the circle: Suppose one knows either the circumference or diameter of a circle. In that case, you can estimate the other one using these equations: Circumference/Diameter = Pi Diameter/Circumference = 2.71 or also if one knows the radius, they can use this equation:

Circumference/Radius = Pi

Radius/Circumference = 3.53


Approximate 3 5/8 radius or circumference

Pi (3.14) is an infinite number that never ends and keeps on continuing without stopping. Pi was first thought of in India around 3000 years ago, but it wasn’t proven by mathematicians until 1761 when they discovered the value to be over 22/7. Even though Pi has been known for a very long time there is still no way to calculate pi because it does not end. However, there are many ways to approximate pi like 355/113 which comes out at 3.141592920353982300884955…

Properties of are of the circle:

  • A circle has 360 degrees in circumference.
  • 1 degree = .01745 radians.
  • A segment is the part of a circle between two points on the circumference.
  • An arc is part of an incomplete circumference, not including the endpoints. An arc may be considered half an angle measured at its center between two points on the circumference.
  • Angles in a segment are measured with respect to the line that joins its endpoints. Segments can also be measured by their central angles (see illustration). Angles in an arc are usually measured with respect to one of its endpoints (angle at endpoint or central angle) or as the measure of the central angle (in radians) formed by connecting each endpoint (angle in the segment or angular distance on the circle).
  • A chord is a line that joins two points on the circumference of a circle. A secant is any line that intersects a circle at two points. The shortest distance between an external point and the circle is called the radius.

A real-life example of circumference and area of a circle:

The circumference: The Sun’s circumference is about 1.4 million kilometers across, but the Earth’s is only 40,075 km because it is smaller in diameter and thus has a smaller circumference. This means that the distance halfway around the world going through both poles is slightly more than 21,600 km (13,400 mi). Also, the circumference of Earth is about 40,000 km (24,900 mi), or almost 25,000 miles.

Area of circle: The area of Earth is about 510 million square kilometers or 196.9 million square miles. Since there are 60 minutes in an hour and 60 seconds in a minute, if you wanted to walk around the equator at 4 mph it would take you slightly over 24 hours (the exact amount of time would depend on your particular speed). It would also take you over 31 days to walk around the world at that speed, meaning that if you walked around the earth on a nonstop tour of 24 hours every day, it would take you more than three months just to finish. A lot can happen in three months.

These topics are very interesting and critical concepts in mathematics, and one surely can learn in detail about these concepts on the Cuemath website.


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