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Math Tricks of Mensuration Formulas, Triangle, Cube, Cuboid, Quadrilateral, Circle, Partnership, Pipe and cistern, Problem on Train and ages, Profit and Loss, simple-Compound interest, Simplification Solved Quantitative Aptitude, Time Speed, Distance, Time and work Age calculation, Average, Boat and Stream, Division rules LCM and HCF Shortcut Formulas.

Cube and Cuboid mensuration formulas of volume, area, surface

New Math Tricks is covering all mensuration topics and tricks. Today, we are going to discuss the properties, shortcuts formula, aptitude question and tricky solution of cube and cuboid mensuration chapter. The tutorial has made from basic level to exam level for your confidence and performance well in the upcoming competitive exam. Before discussing the shortcut formula, we should have the basic concept of cube and Cuboid. So, look at below some basic properties and mensuration formulas of Cube and Cuboid.

Cube and Cuboid properties and formulas

Cube and cuboid are made with height, length and base and six sides (face). And the shape of a cube or cuboid is 3 dimensional. We have covered triangle, circle and quadrilateral which are 2-dimensional shapes.

Look at the below image which are a cube and cuboid forms.


As you have looked the above image where we can see six faces(side). Also, it has vertices. The vertices are the longest line of a cube and cuboid. in competitive math, generally ask volume, area and vertices length. Now we are moving to mensuration formulas for Cube and Cuboid.

Cube mensuration formulas

A cube has 12 equal edges and six faces. As all edges are equal so height, width and base are equal. Therefore, the area of each face also equal. If we have to find the total surface area, we will add areas of all (six) faces. And each face can be calculated as edge^2. So, the shortcut formula for the total surface area of cube became (6 X area of one face) or (6*Edge^2). When we have to calculate the lateral surface area of a cube then we multiply by 4 with the area of one face. Getting confusion with this math tricks? Look at below image to be clear the shortcut formula.

Lateral and Total Surface Area formula of Cube and Cuboid

And the volume of a cube is edge^3 Square unit.

Volume and area formula of cuboid mensuration

Every cube is cuboid but all cuboids are not cubes.  So differently, you should know shortcuts volume and area formula of the cuboid. The difference between cube and cuboid is on edges length. The different length (maximum three variants) may be in cuboid where equal in a cube. So length, base and height may be different. That's why in the formula of the cuboid, becomes different from the cube. 
Cuboid-total-lateral-surface-area-volume-math-tricks-total-surface-lateral surface
So, friend, these are the basic shortcut formulas for the cube and cuboid to calculate volume, area, total surface and lateral surface area of cube and cuboid. In the next tutorial, we will practice some mensuration problems related to the cube and cuboid. Thanks for reading and learning to day's tutorial on cube and cuboid.

Read more Arithmetics Chapter
Boats and Stream

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Circle Mensuration problems with circumference Area formula

We have already covered mensuration formulas related to the circle. Especially, we discussed properties, circumference and area formula of the circle. Today, we are going to solve some mensuration problems from this chapter. This is the third tutorial on circle mensuration. Look at below few questions and easy solution with the mensuration formulas.

Circle Mensuration Solved Math by Shortcuts Formula

►Question 1: A circle which has by 14m long radius. Now, find the area and circumference of the circle.
Solution: This is the simple question from the circle mensuration. Directly, we can apply the circumference formula of the circle. look at below for the easy solution.

We know the circumference of a circle is  2 π r. Where π=22/7 and r is half of the diameter. So, simply apply the formula to find the correct answer.
2π r= 2* (22/7)*14 =88m.
►Area of the Circle: The area formula of a circle is π r^2 when we know the length of the radius. Therefore the Ara of the Circle will be (22/7)*14*14 Sq.m
=28*22 Sq.m  =616 Sqm.
►Question 2: The circumference of a circular park is 440m. Now find the area of the park?
►Easy solution: We knew in the circle mensuration formulas that the area can be calculated directly when the circumference is known. Look at below image for the shortcut formula and solution of this mensuration problem.

►Question 3: A circle has made by a rope. And it's radius was 28m long. If you made a square with that rope, how long will be an arm of the square?
Solution: We have to calculate the area of the circle at first. Then, we can calculate the length of the square. Look at below for the solution.
Question 4: A Cricket playground has made by 63 m radius. If the radius increased by 7m, then find the deference area of the circle?
►Solution: you can solve this mensuration problem by calculating two times area of two circles. But you can answer this question by a single operation. But the question is how it's possible? Look at below for the shortcut mensuration formula for this type of question.
Is not it easy mensuration friends? Keep visiting New Math Tricks for more question and aptitude formulas. You may check all Arithmetics math tricks or some solved math problems.

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Triangle Mensuration Question Answer with Perimeter Area Formula

We learnt mensuration formulas of triangle previously. Today, we are going to solve some important triangle mensuration question answer by perimeter and area formula. if you had not read previous triangle mensuration shortcut formula yet, then visit that by clicking below link.
Classification of Triangles
Triangle mensuration formulas

Triangle Mensuration perimeter Area formula

Look at below for important triangle mensuration question and answer.
Question1: What is the area of a 20 cm equilateral triangle?
Solution: You know that an equilateral triangle is called which all arms are equal. Look at below image for area calculating shortcut formula and the solution of this type of question.
Question 2: A triangle which arms lengths are 20m, 30m and 40 m respectively. Now find the area of that triangles.
Answer: Here, the triangle is the isolateral triangle and we knew all arm lengths. Simply we will sue the hero formula to find the area. Look at below, how we solved the mensuration problems?
We hope, you got the easy solution of the triangle mensuration problem. Here, we have applied the HERON formula. You are seeing the S which value is half of the perimeter of the triangle.
Now look for the next triangle mensuration question and answer.
Question 3: A right angular triangle whose hypotenuse and the base are 6m and 4m respectively. Now find the area of the triangle?
Explanation:  we know the area formula of a triangle is (1/2)*base*height. But in this question height is unknown, though we know the hypotenuse and base. So we need to find the height of the triangle. As you have seen in the tutorial of triangle mensuration formula that the Pythagorean theorem can be used to find the height. So, we used it to find and applied to solve the mensuration. And finally used the formula (1/2)*base*height.
We will post more triangle mensuration question and answer with the mensuration formulas. Now, you may visit chapters-wise arithmetics math tricks or more mensuration formulas from here. 

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Prism Mensuration Formulas concept-Aptitude Tricks

Prism mensuration formulas concept and tricks are very important, and we should know these clearly because several types of prism mensuration problems are asked in the competitive math section. Here, we are going to discuss the prism properties, mensuration formulas and some solved mensuration problems related to this chapter. Look at below for properties of prisms.

We hope, you got the concept by looking the above photo. If not, let me clear the property of prism. Then we will discuss mensuration formulas related to the prism.

Mensuration formulas of a prism

What is Prism?
Prism a type of solid shape which base and top properties are same and all others properties are flat. If you looked the above photo, you can see that every shape have the same base and top properties which are yellow coloured. The top and base property may be formed by a triangle, quadrilateral, pentagonal, hexagonal or octagonal or so on geometrical shapes. And the formula for finding volume or surface area(lateral and total surface area) of a prism depending on base, top and lateral faces properties. This is the core concept for mensuration problems of the prism. Now, we are showing you how different Prism mensuration formulas made and also how to remember these mensuration formulas? To understand the concept of the prism, we used too many words. But in reality, it helps you to clearly understand the prism mensuration formulas and tricks for this chapters problems.
Prism volume formulas(General):  The general volume formula of the prism is (Area of base X Height). Prism has various shapes, according to shapes, formulas are below with the images. We take only those shapes which are important for competitive maths.
Prism area formulas(General): The general area formula of prism(total surface) is (2 X area of  the Base + perimeter of base X height)
The volume of Triangular Prism: Look at below for volume formula of a triangular prism. 

We recommend you to read the tutorial on Triangle mensuration formulas. When you have to find volume or area of a triangular prism then you need the formula of triangle area. As you know triangle are various types according to its arms and angles, we briefly discussed that on triangle tutorial. 
Volume formula of Rectangular Prism:  Here, we are not discussing briefly. Just use the formula of shortcut cuboid volume formulas. Because Cuboid is a prism. But note, when you got non-right angular prism then you have to find the height of the prism.
Soon, we will come back on this topic with other important formulas and concepts.
Read Arithmetic chapter
Problems on trains

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Cylinder mensuration tricks with solved math

Cylinder mensuration is also a valuable math chapter for competitive exams. Here we are going to discuss Cylinder properties, Surface area and volume measurement formula and shortcuts tricks. Look at the below images, it is Cylinder and its properties.
The last mensuration tutorial was on Cube and cuboid mensuration tricks. If you have read that's then you can easily adapt to this tutorial. Because, if We make a cylinder into plane figures then we will get two circles and a rectangular figure. These will help you to find the surface area easily. Generally, in question, two types surface area are asking. They are
1.Total surface area of cylinder
2. Curve surface area of the cylinder.

As you have calculated Lateral and total surface area of Cube and Cuboid. Hope, here no introduction need about the Curve and Total Surface area of Cylinder. Let's move to Formulas.

Cylinder Surface area formula

Cylinder Curve Surface area

The formula for the curve surface area without the yellow portion in above image. As you look at the left-hand side of the cylinder a rectangular picture also laid. The area of the rectangular portion is the Curve Surface area of the cylinder. If we know the height of the cylinder and also the radius of top or bottom circle then easily calculation can be done. Because the area of the rectangular is equal to (Circumference X Height).look at below.

Total surface Area

: You have seen the above images, there are a square or rectangular and two circles. Just add all area of three properties. Look at below how the shortcut formula made in a single formula.
Thanks for being here today, hope you have enjoyed the Cylinder mensuration Shortcut formula. For more mensuration chapters, visit the mensuration tricks section.

Time and Works shortcut formulas

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Mensuration problems and aptitude related to the Square

In the mensuration topic quadrilateral properties and formula, we have briefly discussed the various shape, properties and shortcut formula. Square is one of the important figures of the quadrilateral. Today we are going to solve some mensuration problems related to the square. As you have learnt that the square is four equal-armed and right angular figure. Before going to solve square mensuration, please read the opening tutorial of quadrilateral properties and mensuration tricks if you need.

Square mensuration and math tricks

Mensuration Problem 1: Find the area and perimeter of a 20 metres armed square. 
Solution: Arm length of the square is 20m. So the area will be (Arm * Arm) square unit. So area= 20*20 Sq metre =400 Sq metre.
The perimeter is the outer length of the figure. The perimeter of the square is (4*Arm). So, perimeter = 4*20 = 80 metre.
mensuration problem 2: The diagonal of a square is 10√2. Now find the area of the square.
Solution: Just look at below how we find the area of the square. 
Mensuration problem 3:  20 meters and 40 meters armed two square land marge into a rectangular land, if the base of the rectangular lad is 50 meters then find the width of the land.
Solution: To solve the mensuration problem, we have to calculate the sum of the area of both square and that is the area of rectangular land.  Look at the below how we solved it. 
 Problem 4: A house owner wants to cover a courtyard with marvels. The base and the width of the courtyard are 10 and 8 meters respectively. The area of each marvel is 1/4 sq metre. Then how many marvels should have to buy to cover the courtyard?
Solution: We can solve this mensuration problem easily without pen and paper. First of all, we will calculate the area of the courtyard. As the courtyard is rectangular, so the area can be calculated multiplying by base and width. Area= 10*8 sq metre
=80 sq metre. Now we have to divide the area of the courtyard by the area of a marvel tile. 80/(1/4)=80*4
=320 tile needs to cover the courtyard.

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Triangle math tricks for quantitative aptitudes

Classification and properties of the triangle, we have discussed on the opening tutorial of this topic. Today, we are going to resume triangle mensuration formulas with all math tricks. Triangle math tricks are very important to the point of competitive math. We strongly recommend you to visit Triangle properties and classification for the clear concept. 
Classification and properties of the triangle.

Perimeter area formula of triangle

Perimeter formula for Triangle: The perimeter is the outer length of any figure. So, it easy to find the perimeter of any triangle, when we know all the lengths of arms. Just, we have to add all arm's length. When we got equilateral triangle then we have to multiply an arm by 3. The formula became 3*an arm's length. When we will not get all arm's length then we have to follow the type of triangles or other formulae and then have to apply required formula or concept to find out the perimeter of a triangle. We hope, at the end of this tutorial, you will get it very well. 

Triangle math tricks for area:

We know the above formula for calculating the area of the triangle. Where S represents the half of perimeter of the triangle and a, b and c are the lengths of three arms. This formula can be used to any triangle where we know the perimeter or able to find it. But sometimes, we can use some tricky shortcut formula to find the area of a triangle on some special triangles. Even we can simplify to find the area of a triangle by using some concept of triangles or merging with the quadrilateral figures. 

Area formula for right angle triangle When we know a triangle is right angular and have to calculate it's area, then use the below formula. 


How made the formula? This is a simple fact. Look at below, First one(pic 1) is a right angular triangle and the second one (pic2) is an imaginary figure of rectangular. As you know that the hypotenuse is the longest arm of a triangle as well as rectangular. If you imagine hypotenuse as a diagonal of a rectangular, the figure divides into two equal triangles. the formula of the rectangle is base*width Sq.units. So,  In this logic, you can say that the triangle is the half area of the rectangle. Also, note that all squares are rectangular. 


Above formula, you can apply on any kind of triangle to calculate the area. Because you may have proved in geometry that when a triangle made with same base and height then the triangle will be half of the rectangular in point of the area.

Area formula of Equilateral Triangle: Shortcut area formula of an equilateral triangle is below.

Triangle-mensuration-solved -by-area-formula-math-tricks

In the next tutorial on the triangle, we will apply all formulas to a triangle mensuration problems.

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Solved Arithmetics Questions of exam level Maths in Tricky Method.

We are preparing for quantitative aptitudes with the question-answer series for our upcoming competitive maths. Here, we take the most important math problems which have already asked in previous years competitive exam or a relevant question to perform well in the exam. Look at below, we have solved some exam level arithmetic problems using math tricks. This is the 3rd tutorial on solved quantitative aptitudes. If you hadn't viewed previous two tutorials, then visit by clicking below.

  1. Various types solved question part-1
  2. Solved Question part-2

Tricky Solved Arithmetics Questions

Quantitative question 1: In two blends mixed tea, the ratios of Darjeeling and Assam tea are 4:7 and 2:5. The ratio in which these two blends should be mixed to get the ratio of Darjeeling and Assam tea in the new mixture as 6:13 is-
Solution:  For the quick solution of this problem, we will use the Allegation method.
Problem 2:   Two trains 180 metres and 120 metres in length are running towards each other on parallel rails, the first one at the rate 65 km per hours and second at 55 km per hour. In how many seconds will they can be clear each other from the moment they meet?

Solution: Here, we have to calculate the relative speed. As per the question both trains are not running in the same direction. So, the relative speed of both trains will be the sum of their speed. Relative speed =65+55=120 km per hours. And they have to cover the length of both trains. The sum of both trains length is 180+120 =300 metre. 
Problem 3: A furniture seller allows 4% discount on his marked price. If the cost price of an article is Rs. 8 000  and he has to make a profit of 20%, then how many rupees have to mark as the price of the furniture?
Problem 4: There are 480 coins in half rupees, quarter rupees and 10 paise coins and their values are proportional to 5:3:1. The numbers of coins in each case are 
Solution: The ratio of value = 5:3:1 and ratio of numbers =10:12:10 or 5:6:5.
Therefore, numbers of 50 paise coins = (5/16) *480=5*30=150.
Number of 25 paise coins =(6/16)*480 =6*30=180.
As ration of 10 paise coins and 50 paise coins are equal so it will be same. Therefore, the numbers of 50, 25 and 10 paise coin will be 150,180 and 150 respectively. 

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