Formula for Surface Area Math

Introduction for formula for surface area math:

In math, surface area in a solid, is the sum of the surface areas of all its faces including  the base of the solid. Or surface area means the area of the sides including the top and bottom. Lateral surface area is found for any math geometric figures, around its outer area. Surface area is usually measured in terms of some square units. Let us see surface area formulas and problems in math. I like to share this Find the Surface Area of a Cone with you all through my article.

Formula for Surface Area Math:

Math lateral surface area formulas:

•    Cube = 6a2, where a is the length of a side.

•    Sphere = 4pr2, r is the radius of the sphere.

•    Cone = p rs, where r and s are the radius and slant height of the cone

•    Cylinder = 2pr(r+h), where r is the radius and h is the height of the cylinder

•    Rectangular prism = 2LW+ 2LH +2WH

•    Triangular prism = base area + perimeter × height

•    Pentagonal prism = 5 × area of each rectangle

Examples for lateral surface area in math problems:

Example 1:

Find the surface area of a cube whose side is 7cm

Solution:

Given: side = 7cm

Formula:   Cube = 6a2

= 6(7)2

= 6(49)

= 294cm2

Example 2:

Find the lateral surface area of a pentagonal prism, if a = 5 cm and b = 14 cm.

Solution:

Step 1: In the given figure, the base of the prism is a regular pentagon.

Step 2: All five rectangles of a regular pentagon are congruent.

Step 3: Lateral surface area of the prism = 5 × area of each rectangle

Step 4: = 5 × 5 × 14 [Substitute the values.]

Step 5: = 350

So, Lateral surface area of the pentagonal prism = 350 cm2.

Example Formula for Surface Area Math:

Example 1:

Height and radius of the cone is 5ft and 7ft. Find the surface area of the given cone.

Solution: Lateral surface area of the cone = prs

Step 1:Slant height of the cone, s =v(25+49) [s =vr2+h2.]

s = 8.6ft

Step 2: Lateral surface area = 3.14×7×8.6 [ r = 7 and s = 8.6]

=189.03

So, the lateral surface area of the cone = 189.03square ft.

Example 2:

Find the surface area of a sphere its radius 6cm.

Solution:

Given: radius = 6cm

Formula surface area of a sphere = 4pr2

= 4×3.14× 6× 6

= 200.96

Therefore surface area of sphere = 200.96cm2


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Math practice problem for surface area formula:

1) Find the lateral surface area for of a sphere radius (r) = 3cm ?

2) Find the surface area of a cube side is 9ft?

Answer:

1)113.04cm2

2) 486square ft.

Standard Lines Chords

Introduction to standard lines chords:

Line is fundamental concept in the mathematics. In geometry, line is straight line curve. Line is representing the straight line object. Geometrical object that is straight, infinitely long is called as line. Line is the one dimension figure. Lines have no height and no width. Lines that linking the two points on the circle is the chords. In this article we see detailed about the standard lines chords. Understanding Skew Lines Examples is always challenging for me but thanks to all math help websites to help me out.

Chords:

One of the geometry line segment is the chord of a circle. The line extension of a chord is the secand line.

Example 1: Standard Lines Chords:

Write the equation of the line that passing through the two points are (7, 10) (8, 13). Calculate the slope value of the given points.

Solution:

Given points are (7, 10) (8, 13)

Formula is used to for calculate the slope value of the given points:

m = `(y_2 - y_1) / (x_2 - x_1)`

Here, x1 = 7, x2 = 10, y1 = 8, y2 = 13

Substitute the given value form the above formula:

m = `(13 - 8)/ (10 - 7)`

m = `(5)/ (3)`

m = 1.67

Slope value of these given points is 1.67.

Example 2: Standard Lines Chords:

Find the equation of the line that passing through the two points are (5, 8) and scope value is -2.

Solution:

Given points are (5, 8)

Straight line equation is:

(y - y1) = m (x - x1)

Here x1 = 5, y1 = 8, m = -2.

Substitute these value form the above formula:

(y - 8) = -2 (x - 5)

(y - 8) = -2x + 10

y = -2x + 10 + 8

y = 2x +18

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Example 3: Standard Lines Chords:

Write the equation of the line that passing through the two points are (8, 15) (10, 17). Calculate the slope value of the given points.

Solution:

Given points are (8, 15) (10, 17)

Formula is used to for calculate the slope value of the given points:

m = `(y_2 - y_1) / (x_2 - x_1)`

Here, x1 = 8, x2 = 15, y1 = 10, y2 = 17

Substitute the given value form the above formula:

m = `(17 - 10)/ (15 - 8)`

m = `(7)/ (7)`

m = 1

Slope value of these given points is 1.

Sample Algebra Problems with Answers Help

Introduction to sample algebra problems with answers help:

Let us see about sample algebra problems with answers help in this article. Algebra is one of the main concepts of the mathematics. Algebra is the simple calculation and simple solving system of the equation for particular variable. Algebra includes real number and complex number. Algebra statement is the base on the variable. Letters and symbols are used to calculate the unidentified variable of the given algebra expression.I like to share this Audit Sample Size with you all through my article.

Example 1: Sample Algebra Problems with Answers Help:

To solve: 3(2x + 4) + 5(x + 3) + (4x + 6)

Solution:

Given

3(2x + 4) + 5(x + 3) + (4x + 6)

Multiply the given term:

3(2x + 4) + 5(x + 3) + (4x + 6)

6x + 12 + 5x + 15 + 4x + 6

Terms are grouped:

6x + 12 + 5x + 15 + 4x + 6

6x + 5x + 4x + 12 + 15 + 6

15x + 33

Example 2: Sample Algebra Problems with Answers Help:

To solve following algebra expression: a`xx` (a+7), where value of a =4.

Solution:

Step 1: In this problem given algebra expression is: a`xx` (a+7)

Step 2: Substitute a value from given algebra expression

a`xx` (a + 7) = 4 `xx` (4 + 7)

=4 `xx` (11)

= 44

Step 3: Answer for this given algebra expression is 44. Please express your views of this topic what are adjacent angles by commenting on blog.

Example 3: Sample Algebra Problems with Answers Help:

To solve: 5(x + 1) + 2(2x + 4) + (10x + 6)

Solution:

Step 1:

Given equation is:

5(x + 1) + 2(2x + 4) + (10x + 6)

Step 2:

Multiply the given term:

5(x + 1) + 2(2x + 4) + (10x + 6)

5x + 5 + 4x + 8 + 10x + 6

Step 3:

Terms are grouped:

5x + 5 + 4x + 8 + 10x + 6

5x + 4x + 10x + 5 + 8 + 6

Step 4:

Answer for this problem is

19x + 19

Reading and Writing Relationship

Introduction to reading and writing relationship:

Reading and writing relationship 1:

Reading and writing are two aspects that are entwined in  such a way that each of them is  incomplete without the other. Reading and writing, both contribute significantly to the communication media.Writing requires education(formal/informal), insight and dedication. To write successfully, one must have  strong command over the language that he/she intends to write in, apart from practical knowledge, clarity of thought and the ability to express effectively. In order to gain all these skills, reading  proves to be the easiest way.

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Reading and Writing Relationship :2

Reading helps a prospective writer to develop an understanding of the technicalities of writing on topics of different genres. A  prospective writer should be able to decide what area he/she shall be able to successfully write about. Trying out writing on various disciplines helps one to identify which discipline he/she feels best suits his/her abilities. In order to do so, one must read extensively.

Reading and Writing Relationship :3

Reading enables a person to understand grammar, style, dialect, vocabulary and most of the aspects of literature that are vital to the process of good writing. Reading allows a person to comprehend the expectations of a reader and the specific styles of writing that make the text interesting to the reader. While reading, one must be able to decipher what has been written. On the other hand, a writer needs to make sure that the content of his/her text should communicate with clarity the idea, opinion or the information on a particulat subject. Reading also helps   understand  expression which in turn plays a significant role in writing.

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Reading and Writing Relationship :4

Reading is a stepping stone to successful writing. Reading helps to gain proficiency in being able to understand information which is very important and to know how information is presented in order to make the text easy to understand. Reading is one way by which a writer places himself in the reader’s shoes, thereby, allowing himself to know the extent to which his effort has become successful. The intricate relationship between reading and writing remains an unsolved mystery that is glaringly obvious and cannot be overlooked in any language!!

Solving Variables in Statistics

Introduction of solving variables in statistics

Statistics deals with the collection and analysis of numerical data. Statistics is specifically useful in drawing general conclusions about a set of data from a sample of the data. We can say  Statistics as descriptive statistics and analytical Statistics, Since it is describing the data and drawing conclusions from the data. Statistics can solves problems related to standard deviation, variance, mean, median, binomial coefficient,standard error parameter, sample size, variability coefficient and populations. Understanding What are Variables? is always challenging for me but thanks to all math help websites to help me out.

Formulae

Formulas for solving variables in statistics:

For solving mean m =  `(sum_(k=1)^nxx_(k))/n`
median is the number in the middle

For solving variance v =`(sum_(k=1)^n(x_(k)-m)^2)/(n-1)`
For solving standard deviation s =`sqrt(v)`
By solving the above formulas we get the result of the variables. Is this topic what is a rational number hard for you? Watch out for my coming posts.

Examples of Solving Variables in Statistics:

Now let us see some examples of solving variables in statistics.

How to find Mean?

Consider the series : 15, 18, 22, 20

Here n = 4

The sum : `sum_(k=1)^nx_(k)` =15+18+22+20

By substituting K=1 to 4 we get sum as 75

Mean m = `(sum_(k=1)^nxx_(k))/n` = `75/4`

The Mean or Average is 18.75

How to find Median?

Here take the variable median

Here we  have to take the series in order and there are two case available

Case 1:

Numbers in the series is odd

9, 3, 44, 17, 15

Line up your numbers(smallest to largest): 3, 9, 15, 17, 44

The number in the middle is 15

Median is 15

Case 2:

Numbers in the series is even

8, 3, 44, 17, 12, 6

Line up your numbers: 3, 6, 8, 12, 17, 44

Having 2 middles numbers

Add 8 and 12 and then divide by 2: 8+12 = 20 ÷ 2 = 10

The Median is 10.

How to find Variance?

Here take a variable variance

44,50,38,96,42,47,40,39,46,50

`(44+50+38+96+42+47+40+39+46+50)/10`

Mean m = 49.2

Variance v =`(sum_(k=1)^n(x_(k)-m)^2)/(n-1)` `= 2600.4/(10-1)`

The variance is 289

How to find Standard deviation?

Here take a variable standard deviation

The square root of variance is standard deviation =`sqrt(289)`

The standard deviation is 17

Interior Angle Sum Theorem

Introduction to interior angle sum theorem.

Any plane closed figures formed by straight lines are called polygons.  According to the number of lines used to form the polygon, the polygon gets its name.   If there are three lines, it called a triangle.  To get a closed figure, we need minimum three lines.  If there are four lines in the polygon, it is called as a quadrilateral.  We know that the sum of the interior angles of a triangle is 1800.  Similarly the sum of the interior angles of a quadrilateral is 3600.

A plane figure bounded by straight lines is called a rectilinear figure. A closed plane figure, bounded by at least three line segments is called a polygon. A polygon is named by the number of sides in it, as given below:

1. Convex Polygon: If each angle of a polygon is less than 1800; the polygon is called a convex polygon.

2. Concave Polygon: If at least one angle of a polygon is greater than 1800; it is called a concave polygon.

Unless otherwise stated, a polygon means a convex polygon.

In a polygon of 'n' sides, the sum of the interior angles is equal to (2n – 4) right angles. This is the interior angle sum theorem. Is this topic parts of a circle hard for you? Watch out for my coming posts.

Example Problems on Interior Angle Sum Theorem:

Ex 1: Find the sum of the interior angles of a polygon of 10 sides.

Solution: The sum of the interior angles with n sides = (2n = 4) `xx ` 90.

Here n = 10 sides,                                                              = (2 (10) – 4) `xx` 90.

= (20 - 4) x 90

= 16 `xx ` 90.

= 14400.

Ex 2: In a pentagon ABCDE; AB is parallel to ED and angle B = 1400. Find the angles C and D, if |_C: |_D = 5: 6.

Solution : Since, `[AB]/[ED]`` implies` |_A + |_E = 1800.

Given: |_C : |_D = 5 : 6 `implies` if |_C = 5x, |_D = 6x.

Now. |_A + |_B + |_c + |_D + |_E = (2 `xx` 5 – 4)` xx` 900.

`implies ` (|_A + |_E) + 1400 + 5x + 6x = 5400

`implies ` 1800 + 1400 + 5x + 6x = 5400

That is 11x = 5400 – 3200 `implies ` 11x = 2200 and x = `220^0/ 11` = 200.

Therefore |_C = 5x = 5` xx` 200 = 1000 and |_D = 6x = 6 `xx` 200 = 1200.

Ex 3: The sum of the interior angles of a polygon is five times the sum of its exterior angles.  Find the number of sides in the polygon.

Solution: Let the number of sides by n.

Given: The sum of the interior angles of the polygon

= 5` xx` the sum of its exterior angle.

Therefore (2n – 4) `xx ` 900 = 5 `xx` `360^0`

(2n - 4) = 5 x 4   [ since 360 / 90 = 4]

2n - 4 = 20

On solving, we get:   2n = 24 and n = 12.

Therefore the required number of sides in the polygon = 12.

Practice Problems on Interior Angles Sum Theorem.

1. The angle of a pentagon are in the ratio 4: 8: 6: 4: 5.  Find each angle of the pentagon.

[Ans: 80, 160, 120, 80 and 100]

2. In a polygon there are 5 right angles and the remaining angles are equal to 1950 each.

Find the number of sides in the polygon.

[Ans: 11]

Probability and Statistical Inference

Introduction to Probability and Statistical inference

In math, probability is a way of expressing knowledge or principle that an event will happen or has occurred. Statistical is the proper science of making successful use of mathematical data relating to groups of individuals or experiments. Now we will see the inference and examples of the probability and statistical. Understanding Continuous Probability Distribution is always challenging for me but thanks to all math help websites to help me out.

Example for Probability Inference

In a bag, there are 25 roses available. In that roses there are 10 white colour roses, 8 orange colour roses and 7 red colour roses. Solve the probability if we,

i) Choose the white colour rose.

ii) Choose the red colour rose.

Solution

Total roses n(S) = 25

White roses n (A) = 10

Orange roses n (B) =8

Red roses n(C) = 7

i) Assume the P(A) is the probability for choose white rose .

P(A)= `(n(A))/(n(S))`

= `(10)/(25)`

= `(2)/(5)`

ii) Assume the P(C) is the probability for choose red rose.

P(C) =`(n(C))/(n(S))`

=.`(7)/(25)`

Example for Statistical Inference

Solve the mean, median, mode and range with the following number terms in statistical?

13,16,19,33,35.

Solution

The given numbers are 13,16,19,33,35.

Mean

Normally mean is the average of the number. We need to solve the sum of the given number for find the average. Is this topic Linear Regression Calculator hard for you? Watch out for my coming posts.

Sum of the given numbers are = 13+16+19+33+35

= 116.

Now divided by 5(Note: 5 is the total given number of  total) = 116/5

= 23.2

Median

Center value of the given number series is known as median.

The number series is 13,16,19,33,35.

The center value of the above series is 19.

Therefore the median value is 19.

Mode

Mode is a numerous value of the given number series. In this series no repeated value.

Therefore the mode is null.

Range

The difference between greatest value and the smallest value is said to be as the range of the series.

Range = 35-13

=22.

So 22 is the range of the series.

These are the examples for probability and statistical inference.

Equivalent decimals

In our daily life, we go through many circumstances where we need to divide something in parts. If a glass of milk is given and you had one fourth of it, then we can say that you have consumed 0.25 of the glass.1/4 here I a fraction and 0.25 is considered as a decimal number. Decimal numbers are the numbers that are written in parts or in fractions. For example: - ¼ is written as 0.25. Equivalent Decimals are decimals which have same value. Decimal Equivalent scan be converted to fractions.

Just like ½ can be written as 0.5 or 0.5 can be written as ½.Equi decimals can be represented in various ways. We can add any number of zeroes to the decimal number and that will make no difference to the original number. For example: - If we have 3.6, if we add zeroes to this number that will make no difference to the original number that is 3.6. So we can say that 3.6 as equal to 3.60 or 3.600 or 3.6000. We can add any number of zeroes to it.
Hence they will be termed as equival decimals.
Equival decimal form of ½ is 0.5 and of 5/10 is also 0.5. Decimal Equivalent can be expressed as fractions too. For example: - 0.4 is written as 4/10 which can be simplified to 2/5. Similarly 0.400 to means 400/1000 which can be again are simplified to 2/5.
The only way to rewrite decimal is by adding zeroes at the end of the last digit. The number remains same no matter how much zeroes you add. Having problem with Sum of Poisson Random Variables keep reading my upcoming posts, i will try to help you.

Decimal Equivalent Chart shows the answer to the question of What is an Equivalent Decimal exactly. Few of the examples are shown below: -
0.5 = 0.50 = 0.5000 = 0.50000
0.32 = 0.320 = 0.3200 = 0.32000
Some of the examples of equiva decimals and fractions are given below: -
½ = 2/4 = 5/10 which can be written as 0.5 or 0.50, you can add any number of zeroes
¼ = 2/8 = 3/12 which can be written as 0.25 or 0.250.
Hence we can add or remove any number of zeroes to the decimal number without making any change to it. For example: - 3.780 can be written as 3.78. They both have the same value and are considered to be equivalent. Hence we can convert decimal to equi. Decimals by adding and removing zeroes to it.

Pi Infinite Series

Introduction pi (π) infinite series:

In this article we shall discuss about pi (π) infinite series. A number Π (sometimes note down as pi) is a numerical constant whose value is the ratio of every circle's circumference to its diameter in Euclidean space; this is the like worth as the ratio of a circle's area to the four-sided figure of its radius. It is just about equivalent to 3.141593 in the common decimal notation. Having problem with Infinite Sum keep reading my upcoming posts, i will try to help you.

Pi (π) Infinite Series is Irrational Number:

The infinite series of Pi is an Irrational number. So, Irrational number is given below that,

Designed for a lot of centuries previous to the real evidence, mathematicians have consideration that pi was an irrational number. The initial effort at confirmation was through Johann Heinrich Lambert in 1761. From side to side a complex technique he recognized that if x is rational, `tan(x)` have to be irrational. It goes after that if `tan(x)` is rational, x have to be irrational. Because `tan (pi/2)` = 1, `pi/2` should be irrational; thus, pi should be irrational.Please express your views of this topic solving math word problems step by step by commenting on blog.

A lot of people saying Lambert's evidence as too simplified an answer for such a complex and long-lived problem. In 1794, though, A. M. Legendre establishes one more evidence which reverse Lambert up. This original evidence as well go as far as to establish that π2 (pi2) were also irrational.

Notation for Pi (π) Infinite Series:

The notation for pi (π) infinite series is given below that,

Other than a few numerals cannot be note down as a quantity of two digits they are called Irrational Number (π).

Example for pi (π) infinite series irrational number π (Pi) = 3.14159265358979323846264…,

We cannot note down an easy division that equals Pi. The pi irrational number denoted as `22 / 7.`

The accepted rough calculation for pi (π) infinite series = 3.141592653589793238462643383 is closed but not precise.

At the present, infinite series value of pi (π) is given below that π (Pi) = `22 / 7` = 3.14159265358979323846264.

The above value is pi (π) infinite series.