Area of a circle

Hi Friends,

In our previous blog we learned about "An arc of a Circle". Now let us learn about " Area Of A Circle".

A circle is a simple shape of Euclidean geometry consisting of those points in planes which are equidistant from a given point called the center. The common distance of the points of a circle from its center is called its radius. Circles are simple closed curves which divide the plane into two regions, an interior and an exterior.

Example

The diameter of a circle is 8 centimeters. What is the area?

According to the question, diameter = 8 centimeters so, radius = diameter/2

radius = 8/2 centimeters

radius = 4 centimeters

A = ╥x r²

Now put the value of radius = 4 centimeters and ╥= 3.14

Area = 3.14 x (4 cm) x (4 cm)

Therefore, area = 50.24 cm²

By cutting a circle into slices and rearranging those slices to form a rectangle, we can find the area of the circle by finding the area of the rectangle.

Example 1 divides the circle into 8 slices. Move the slices to fit them to the rectangle. They will snap into place. But 8 slices does not give us a very good rectangle. Try example 2, which divides the circle into 12 slices.

The more slices we have, the better the rectangle will be. Try using 24 slices in example 3. Compare the area of the rectangle to the area of the circle. The radius of the circle is equal to the height of the rectangle. The width of the rectangle is equal to 1/2 of the circumference or πr.

Keep reading and leave your comments.

Perimeters

Let us learn what is perimeter,

The term perimeter refers either to the curve constituting the boundary of a lamina, or else to the length of this boundary.

The perimeter of a circle is called the circumference.

The perimeters of some common laminas are summarized in the table below. In the table, e is the eccentricity of an ellipse, a is its semimajor axis, and E(k) is a complete elliptic integral of the second kind.
I hope the above explanation was useful.

Area of circle

Let us study about area of circle,
The distance around a circle is called its circumference. The distance across a circle through its center is called its diameter. We use the Greek letter π (pronounced Pi) to represent the ratio of the circumference of a circle to the diameter. In the last lesson, we learned that the formula for circumference of a circle is: C = πd. For simplicity, we use π = 3.14. We know from the last lesson that the diameter of a circle is twice as long as the radius. This relationship is expressed in the following formula: d = 2r

The area of a circle is the number of square units inside that circle. If each square in the circle to the left has an area of 1 cm², you could count the total number of squares to get the area of this circle. Thus, if there were a total of 28.26 squares, the area of this circle would be 28.26 cm² However, it is easier to use one of the following formulas:


if the radius of this circle is r, the area, A of the circle will be:
A = πr²
a circle with the radius r

where π is a constant that is approximately equals to 3.14.


I hope the above explanation was useful.

Frequency Polygon

Let us study about Frequency polygon,
Relative frequencies of class intervals can also be shown in a frequency polygon. In this chart, the frequency of each class is indicated by points or dots drawn at the midpoints of each class interval. Those points are then connected by straight lines.

The frequency polygon shown in Figure 1 uses points, rather than the bars you would find in a frequency histogram.Figure 1

Frequency polygon display of items sold at a garage sale.

Whether to use bar charts or histograms depends on the data. For example, you may have qualitative data—numerical information about categories that vary significantly in kind. For instance, gender (male or female), types of automobile owned (sedan, sports car, pickup truck, van, and so forth), and religious affiliations (Christian, Jewish, Moslem, and so forth) are all qualitative data. On the other hand, quantitative data can be measured in amounts: age in years, annual salaries, inches of rainfall. Typically, qualitative data are better displayed in bar charts, quantitative data in histograms. As you will see, histograms play an extremely important role in statistics.
Hope the above explanation was useful.

Statistical Probability

Let us study about Statistical Probability,
One of the most familiar uses of statistics is to determine the chance of some occurrence. For instance, what are the chances that it will rain tomorrow or that the Boston Red Sox will win a World Series? These kinds of probabilities, although interesting, are not the variety under discussion here. Rather, we are examining the probability in statistics that deals with classic theory and frequency theory—events that can be repeated over and over again, independently, and under the same conditions.

Coin tossing and card drawing are two such examples. A fair coin (one that is not weighted or fixed) has an equal chance of landing heads as landing tails. A typical deck of cards has 52 different cards—13 of each suit (hearts, clubs, diamonds, and spades)—and each card or suit has an equal chance of being drawn. This kind of event forms the basis of your understanding of probability and enables you to find solutions to everyday problems that seem far removed from coin tossing or card drawing.
Hope the above explanation was useful.

Classification of Fraction

Let Us Learn About Fraction and Classification of Fraction.


The word fraction has been derived from the Latin word fractus, means broken

A Fraction means a part of a group or a region or a whole.

Lets take a apple and cut it into 2 piece

2/4 obtained when we divide a whole apple into 4 equal parts


Now let us cut apple into 10 pieces









10/4 obtained when we divide a whole apple into 10 equal parts

Classification of fractions:

Fractions are classified into:

(i) Decimal fractions

(ii) Vulgar fractions

(iii) Proper fractions

(iv) Improper fractions

(v) Mixed Fractions

(vi) Like fractions

(vii) Unlike fractions

In our next blog we shall learn on Decimal Fraction.

Keep readying and leave your comments.

Law of Cosines

Let us study the law of Cosines,
If α, β, and γ are the angles of any (right, acute, or obtuse) triangle, and a, b, and c are the lengths of the three sides opposite α, β, and γ, respectively, then


These three formulas are called the Law of Cosines. Each follows from the distance formula and is illustrated in Figure 1 .

Figure 1

Reference triangle for Law of Cosines.

From the figure,

Thus the coordinates of A are Remember, all three forms of the Law of Cosines are true even if γ is acute. Using the distance formula, In the preceding formula, if γ is 90°, then the cos 90° = 0, yielding the Pythagoras theorem for right triangles. If the orientation of the triangle is changed to have A or B at the origin, then the other two versions of the Law of Cosines can be obtained. Two specific cases are of particular importance. First, use the Law of Cosines to solve a triangle if the length of the three sides is known. Hope the above explanation was helpful.