Mensuration Formulas for 2D and 3D Shapes (2023)

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  • Last Modified 09-10-2022

Mensuration Formulas for 2D and 3D Shapes (1)

Mensuration Formulas: Mensuration is a branch of mathematics that deals with the area, perimeter, volume, and surface area of various geometrical shapes. It is one of the most important chapters covered in high school Mathematics. Mensuration has immense practical applications in our day-to-day life. It is, for this reason, advanced concepts related to mensuration are covered in higher grades. Knowing the basics of ‘what is mensuration?’ is the key to understand it.

It is also an important and scoring topic for competitive exams, like the Olympiads and NTSE. Mensuration problems are asked in various government job exams as well, like SSC, Banking, Insurance, etc. So it becomes very important for everyone to understand and memorize various mensuration formulas for all 2D and 3D geometrical figures. Keep reading to know more about what is mensuration and mensuration all formula.

Mensuration Formulas for 2D and 3D Shapes (2)

Practice Important Questions On Mensuration Now

Mensuration Formula List: What is Mensuration 2D & 3D Shapes

Mensuration is the branch of mathematics in which we study the surface area, volume, perimeter, length, breadth, and height of geometric shapes. Shapes can be 2D or 3D in nature. Let’s understand what are 2-dimensional and 3-dimensional shapes and what are the differences?

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What is mensuration formula for a 2D Shape?

In geometry, a two-dimensional shape or 2D shape is defined as a flat plane figure or a shape that has only two dimensions. These shapes can be represented in a plane with X-axis and Y-axis. Some common examples of 2D shapes are circle, square, rectangle, parallelogram, and rhombus.

(Video) Mensuration 2D and 3D All Formulas | Mensuration Maths Tricks | Mensuration Formula Tricks

What is mensuration formula for a 3D Shape?

A three-dimensional shape or 3D shape is defined as a solid figure or an object that has three dimensions – length, breadth, and height. Three-dimensional shapes can’t be represented on a plane. We need spatial representation for 3D shapes because they have an extra dimension as thickness or depth.

Mensuration Formulas for 2D and 3D Shapes (3)

Let’s see the major differences between a 2D and a 3D shape:

2D Shape3D Shape
A 2D shape is surrounded by 3 or more straight lines that can be represented on a plane surface.A 3D shape is surrounded by multiple surfaces or planes. They are represented spatially.
2D shapes have only length and breadth, and no height.3D shapes are solid figures and they have an extra dimension as depth or height.
For 2D shapes, we measure the area and perimeter of figures.For 3D shapes, we measure their volume, curved surface area, and total surface area.

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Mensuration Formulas of 2D Geometric Figures

The table below shows the area and perimeter formulas of common 2-D geometrical figures:

Mensuration Formulas for Different 2D Geometric Shapes
ShapeArea FormulaPerimeter FormulaFigure
Square

\({{a}^{2}}\)

\(4a\)

Mensuration Formulas for 2D and 3D Shapes (4)
Rectangle

\(lw\)

\(2(l+w)\)

Mensuration Formulas for 2D and 3D Shapes (5)
Right-angled Triangle

\(\frac{1}{2}bh\)

\(b+h+H\)
where,
H is Hypotenuse

Mensuration Formulas for 2D and 3D Shapes (6)
Scalene Triangle

\(\sqrt{s(s-a)(s-b)(s-c)}\),
where
\(s=\frac{a+b+c}{2}\)

\(a+b+c\)

Mensuration Formulas for 2D and 3D Shapes (7)
Isosceles Triangle

\(\frac{1}{2}bh\)

\(2a+b\)

Mensuration Formulas for 2D and 3D Shapes (8)
Equilateral Triangle

\(\frac{\sqrt{3}}{4}{{a}^{2}}\)

\(3a\)

Mensuration Formulas for 2D and 3D Shapes (9)
Parallelogram

\(bh\)

\(2(a+b)\)

Mensuration Formulas for 2D and 3D Shapes (10)
Trapezium

\(\frac{1}{2}h(a+c)\)

\(a+b+c+d\)

Mensuration Formulas for 2D and 3D Shapes (11)
Rhombus

\(\frac{1}{2}{{d}_{1}}{{d}_{2}}\)

\(4a\)

Mensuration Formulas for 2D and 3D Shapes (12)
Circle

\(\pi{{r}^{2}}\)

\(C=2\pi r\),
where C is the circumference

Mensuration Formulas for 2D and 3D Shapes (13)
Mensuration Formulas for 2D and 3D Shapes (14)

Check the properties of different geometric shapes:

Properties of RhombusProperties of Parallelogram
Properties of QuadrilateralsProperties of Rectangle

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Mensuration Formula Chart: Mensuration Formulas of 3D Geometric Figures

The table below shows the formulas for volume, curved surface area, and total surface area of common 3D geometrical figures:

Mensuration Formulas for Different 3D Geometric Shapes
ShapeVolume FormulaCurved Surface Area FormulaTotal Surface AreaFigure
Cube

\({{a}^{3}}\)

\(4{{a}^{2}}\)

\(6{{a}^{2}}\)

Mensuration Formulas for 2D and 3D Shapes (15)
Cuboid

\(lbh\)

\(2(l+b)h\)

\(2(lb+bh+hl)\)

Mensuration Formulas for 2D and 3D Shapes (16)
Sphere

\(\frac{4}{3}\pi{{r}^{3}}\)

\(4\pi{{r}^{2}}\)

\(4\pi{{r}^{2}}\)

Mensuration Formulas for 2D and 3D Shapes (17)
Hemisphere

\(\frac{2}{3}\pi{{r}^{3}}\)

\(2\pi{{r}^{2}}\)

\(3\pi{{r}^{2}}\)

Mensuration Formulas for 2D and 3D Shapes (18)
Cylinder

\(\pi{{r}^{2}}h\)

\(2\pi rh\)

\(2\pi rh+2\pi{{r}^{2}}\)

Mensuration Formulas for 2D and 3D Shapes (19)
Cone

\(\frac{1}{3}\pi{{r}^{2}}h\)

\(\pi rl\)

\(\pi r(r+l)\)

Mensuration Formulas for 2D and 3D Shapes (20)

Mensuration Formulas PDF: Important Concepts in Mensuration

In mensuration, we come across different terminologies such as area, perimeter, surface area, volume, etc. We have provided definitions for all these terms so that you can be confident about all the mensuration concepts.

    1. Area: Area of a closed 2D geometric shape is defined as the total surface covered by the shape. It is denoted by A. We measure area in m2 or cm2. Remember that area is always measured in square units.
    1. Perimeter: We define perimeter of a closed 2D geometric shape as the total length of its boundary. Perimeter is generally denoted by P. It is measured in m or cm.
    1. Volume: Volume of a 3D geometric shape is defined as the total space occupied by the object. It is always measured in cube units. Common measurement units are m3 or cm3. We denote volume of a solid figure by V.
    1. Curved Surface Area: Curved surface area is used for curved objects such as sphere. It is defined as the total area covered by the curved part of the object. We denote curved surface area by CSA. Since it is a type of area, CSA is also measured in square units (m2 or cm2).
    1. Lateral Surface Area: Lateral surface area is defined as the area occupied by the lateral part of a 3D geometric shape. It is denoted by LSA. We measure lateral surface area in square units (m2 or cm2).
  1. Total Surface Area: When we combine the curved surface area and the lateral surface area of a 3D geometric shape, we get its total surface area (TSA). It is also measured in square units.

Some Other Important Mensuration Formulas

  1. Area of Pathway running across the middle of a rectangle = w (l + b – w)
  2. Perimeter of Pathway around a rectangle field = 2 (l + b + 4w)
  3. Area of Pathway around a rectangle field = 2w (l + b + 2w)
  4. Perimeter of Pathway inside a rectangle field = 2 (l + b – 4w)
  5. Area of Pathway inside a rectangle field = 2w (l + b – 2w)
  6. Area of four walls = 2h (l + b)

Solved Problems on Mensuration Formulas

Here we have provided some mensuration problems with solutions.

Question 1: PQRS is a rectangle. The ratio of the sides PQ and QR is 3:1. If the length of the diagonal PR is 10 cm, then what is the area (in cm²) of the rectangle?

(Video) 3D Shapes - Faces, Edges, and Vertices - Euler's Formula - Geometry

Solution: PQRS is a rectangle

Mensuration Formulas for 2D and 3D Shapes (21)

PR = 10 given
PQ : QR = 3 : 1
In ∆PQR
9x² + x² = 100
10x² = 100
x = √10
Area of rectangle = 3x × 1x
= 3x²
= 3 × 10
= 30

Question 2: The height of a cone is 24 cm and the area of the base is 154 cm². What is the curved surface area (in cm²) of the cone?

Solution: Area of base = 154 cm²
πr² = 154
22/7×r^2
=154
r = 7
Height = 24
Radius = 7
Slant height (ℓ) = √(h²+r² )
ℓ =√(24²+7² )
ℓ=25
C.S.A. = πrℓ
= 22/7×7×25
C.S.A. ⇒ 550 cm²

Question 3: ABCD is a trapezium. Sides AB and CD are parallel to each other. AB = 6 cm, CD = 18 cm, BC = 8 cm and AD = 12 cm. A line parallel to AB divides the trapezium in two parts of equal perimeter. This line cuts BC at E and AD at F. If BE/EC = AF/FD, than what is the value of BE/EC?

Solution: Let BE = x then EC = 8 – x

Mensuration Formulas for 2D and 3D Shapes (22)

BE/EC = AF/FD (Given)
Reverse the given condition & add 1 both side
EC/BE + 1 = FD/AF + 1
(EC+BE)/BE = (FD+AF)/AF
⇒ BC/BE = AD/AF … (i)
Put values in eq. (i)
→ 8/x = 12/AF
AF = 3x/2
Similarly, FD = 12–3x/2
Now perimeter FABE = FECD
FA + AB + BE + FE = EC + CD + DF + FE
3x/2 + 6 + x = 8 – x + 18 + (12–3x/2)
5x = 32
x = 32/5
=BE
Hence EC = 8 –32/5
= 8/5
∴ BE/EC = (32/5)/(8/5)
=4

Question 4: Find the area and perimeter of a square whose side is 10 cm.

(Video) All Mensuration Formulas || 2D and 3D Shapes || Mensuration ||

Solution: Given: Side = a = 10 cm
Area of a square = a2square units
Substitute the value of “a” in the formula, we get
Area of a square = 102
A = 10 x 10 = 100
Therefore, the area of a square = 100 cm2
The perimeter of a square = 4a units
P = 4 x 10 =40
Therefore, the perimeter of a square = 40 cm.

Question 5: Find out the height of a cylinder with a circular base of radius 70 cm and volume 154000 cubic cm.

Solution: Given, r= 70 cm
V= 154000 cm3
Since formula is,
V = πr2h
h = V/πr2
= 154000/15400
=10
Hence, height of the cylinder is 10 cm.

Question 6: If the sides of a triangle are 26 cm, 24 cm, and 10 cm, what is its area?

Solution: The triangle with sides 26 cm, 24 cm and 10 cm is right-angled, where the hypotenuse is 26 cm.
Area of the triangle = 1/2 * 24 * 10 = 120 cm2

Question 7: Find the area of a trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.

Solution: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (20 + 18) * (15)
= 285 cm2

Question 8: Find the area of a parallelogram with a base of 24 cm and a height of 16 cm.

Solution: Area of a parallelogram = base * height
= 24 * 16
= 384 cm2

At Embibe, you can solve mensuration practice questions for free:

(Video) Mensuration Formulas for 3D Shapes Mensuration Formula in Hindi

Class 8 Mensuration Practice Questions
Class 9 Mensuration Practice Questions
Class 10 Mensuration Practice Questions

Check other important Maths articles:

Algebra FormulasLog Table
Geometry FormulasProbability Formula
Arithmetic Progression FormulasCompound Interest Formula
Trigonometry FormulasPermutation and Combination
HCF and LCMDifferentiation Formulas

Frequently Asked Questions on Mensuration Formulas

Students can find some general FAQs on the topic down below:

Q.1: What is the formula for mensuration?
Ans: Mensuration is commonly referred to as the study of geometry and the formulas that come under it involving the calculation of Area, Perimeter, Volume, and Surface Area of different types of 2D and 3D figures. For the full list of formulas, you can refer to this article.

Q.2: How can we remember mensuration formulas?
Ans: The best way to remember mensuration formulas would be by understanding area and perimeter concepts and then using the formula tables provided in this article. You can either take a printout of the page or bookmark it whenever you need it.

Q.3: Which is the easiest way of learning mensuration formulas?
Ans: The easiest way of learning mensuration formulas will be by taking the printout of the formulas provided in this article and sticking them near your study table so that you can revise them whenever you want or you can bookmark this page and visit for revision.

Q.4: Is there any difference between mensuration and geometry?
Ans: Mensuration deals with the calculation of perimeter, area, volume, and other parameters for 2D or 3D geometric shapes. Geometry is concerned with the properties and relations of points and lines of various shapes.

Q.5: What are 2D and 3D mensuration?
Ans: 2D mensuration deals with the area, perimeter, volume, and other parameters related to 2D geometric shapes such as square, rectangle, rhombus, circle, etc.
On the other hand, 3D mensuration is concerned with the calculation of volume, curved surface area, lateral surface area, and total surface area of 3D geometric shapes such as a sphere, cylinder, cone, etc.

Test Your Knowledge of Mensuration With Free Mock Test

Class 8 Maths Practice Questions

Class 8 Maths Mock Test

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Class 9 Maths Mock Test

Class 10 Maths Practice Questions

Class 10 Maths Mock Test

Maths Practice Questions for Class 12

Maths Mock Test for Class 12

Now you are provided with all the necessary information regarding different mensuration formulas. Practice more questions and master this concept. Students can make use ofNCERT Solutionsfor Maths provided by Embibe for their exam preparation.

We hope this detailed list of mensuration formulas help you. If you have any queries, feel free to ask in the comment section below. We will get back to you at the earliest.

(Video) Mensuration 2D and 3D Complete Chapter | All Formulas & Questions | Banking/SSC/Railway | Kaushik |

FAQs

What is 2D and 3D in mensuration? ›

If a shape is surrounded by three or more straight lines in a plane, then it is a 2D shape. If a shape is surrounded by a no. of surfaces or planes then it is a 3D shape. These shapes have no depth or height.

What is the easiest way to learn all mensuration formulas? ›

Plus 1 by 3 PI R 1 into R 2 into n like r1 multiplied with R 1 2 R 1 square in the second term R 2

What is the all formula of mensuration? ›

Mensuration Formulas for 2-D Figures
Mensuration Formulas for 2-Dimensional Figures
ShapeAreaPerimeter
Isosceles Triangle½ × base × height2a + b (sum of sides)
Equilateral Triangle(√3/4) × (side)²3 × side
Right Angled Triangle½ × base × hypotenuseA + B + hypotenuse, where the hypotenuse is √A²+B²
7 more rows

What are the formulas of mensuration Class 6? ›

Mensuration Formulas for Two dimensional Figures
2-Dimensional FiguresArea (Sq.units)Perimeter (Units)
Square( s i d e ) 24 x side
Triangle½ ( b x h )Sum of all sides
Rectanglelength x breadth2 ( length + breadth )
Circleπ r 22 π r

What is mensuration PDF? ›

Mensuration is the branch of mathematics which deals with the study of different geometrical shapes, their areas and volumes in the broadest sense, it is all about the process of measurement. These are two types of geometrical shapes (1) 2D (2) 3D. Perimeter: Perimeter is sum of all the sides.

What is Polygon formula? ›

Polygon Formula

The sum of interior angles of a polygon with “n” sides =180°(n-2) Number of diagonals of a “n-sided” polygon = [n(n-3)]/2. The measure of interior angles of a regular n-sided polygon = [(n-2)180°]/n. The measure of exterior angles of a regular n-sided polygon = 360°/n.

How do I get good at mensuration? ›

To solve the Mensuration Problems, all you need is to learn the formulas and a lot of practice. You can use the sticky notes in your room to learn these formulas. Use mock test papers for practice. At least 3-4 test series should be attempted by an aspirant in a day for best results.

Why area of square is a2? ›

Why is the area of a square a side square? A square is a 2D figure in which all the sides are of equal measure. Since all the sides are equal, the area would be length times width, which is equal to side × side. Hence, the area of a square is side square.

Who invented mensuration? ›

Thus, mensuration refers to the field of geometry that is involved in determining lengths and volumes. It provides the basis for computation and explains the basic equations and properties of many figures and forms. Leonard Digges is the father of Mensuration, while Archimedes invented it.

What is menstruation math? ›

Mensuration is a division of mathematics that studies geometric figure calculation and its parameters such as area, length, volume, lateral surface area, surface area, etc. It outlines the principles of calculation and discusses all the essential equations and properties of various geometric shapes and figures.

Why do we study mensuration? ›

Mensuration is an important topic with high applicability in real-life scenarios. Given below are some of the scenarios. Measurement of agricultural fields, floor areas required for purchase/selling transactions. Measurement of volumes required for packaging milk, liquids, solid edible food items.

What are the formulas of mensuration Class 8? ›

Mensuration Class 8 Formulas
Area of Trapeziumheight x (sum of parallel sides)/2
Surface area of cylinder2πr(r + h)
Volume of Cuboidl × b × h
Volume of Cubea3
Volume of cylinderπr2h
4 more rows
19 Feb 2021

What is the basic formula of maths? ›

List of Maths Formulas (for All Concepts)
2cosacosb Formula30-60-90 Formulas
Area FormulasArea of a Circle Formula
Area of a Pentagon FormulaArea Of A Sector Of A Circle Formula
Area of a Square FormulaArea of a Trapezoid Formula
Area Of An Octagon FormulaArea of Regular Polygon Formula
145 more rows

What is square formula? ›

The Formula for the Area of A Square

The area of a square is equal to (side) × (side) square units. The area of a square when the diagonal, d, is given is d2÷2 square units. For example, The area of a square with each side 8 feet long is 8 × 8 or 64 square feet (ft2).

What is the formula of square for Class 6? ›

We see square is nothing but a rectangle whose length and breadthare equal. So, Area of square = side × side.

Do boys have cramps? ›

Men experience similar symptoms to women when they go through hormonal imbalances. Many of them are similar to the female menstrual cycle including tiredness, cramps, increase sensitivity and cravings. According to one study, around 26 % of men experience these regular “man periods.”

What is menstruation Class 8? ›

Menstruation is the breakdown of the uterus' endometrial lining and blood vessels, resulting in a liquid that is expelled through the vaginal canal. The menstrual flow lasts for three to five days. Menstruation occurs every 28/29 days in human females. If the released ovum is not fertilized, menstruation begins.

What is menstruation Class 12? ›

Menstruation cycle takes place in the endometrium of the uterus. It is the monthly discharge of blood and mucosal tissues shed from the inner lining of the uterus. It is also known as period or monthly as it occurs once in a month and is the most visible phase of the menstrual cycle.

What is the cube formula? ›

Length = Breadth = Height = a. Thus, the measure of each edge of the cube = a. Therefore, the volume of cube formula is a × a × a = a3. It is to be noted that the number obtained using cube formula is the perfect cube number.

What is a 250 sided polygon called? ›

A regular chiliagon is represented by Schläfli symbol {1,000} and can be constructed as a truncated 500-gon, t{500}, or a twice-truncated 250-gon, tt{250}, or a thrice-truncated 125-gon, ttt{125}.

What is the formula of triangular? ›

The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h. This formula is applicable to all types of triangles, whether it is a scalene triangle, an isosceles triangle, or an equilateral triangle.

Why does menstruation occur in females? ›

The egg travels through a thin tube called a fallopian tube to the uterus. If the egg is fertilized by a sperm cell, it attaches to the wall of the uterus, where over time it develops into a baby. If the egg is not fertilized, the uterus lining breaks down and bleeds, causing a period.

How do you solve period problems? ›

How to get regular periods naturally
  1. Practice yoga. Yoga may be an effective treatment for different menstrual issues. ...
  2. Maintain a healthy weight. ...
  3. Exercise regularly. ...
  4. Spice things up with ginger. ...
  5. Add some cinnamon. ...
  6. Get your daily dose of vitamins for a healthy period. ...
  7. Drink apple cider vinegar daily. ...
  8. Eat pineapple.

How long does your menstrual cycle last? ›

In your 20s and 30s, your cycles are usually regular and can last anywhere from 24 to 38 days. In your 40s, as your body starts the transition to menopause, your cycles might become irregular. Your menstrual periods might stop for a month or a few months and then start again.

How do you find the area of a triangle in a circle? ›

Calculating area of a Triangle in a Circle - YouTube

How do you figure volume of a cube? ›

The formula of volume of the cube is given by: Volume = a3, where a is the length of its sides or edges.

How do u find area of triangle? ›

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.

Who is the father of maths? ›

Who is Archimedes? The Father of Math is the great Greek mathematician and philosopher Archimedes.

Who is father of trigonometry? ›

The first known table of chords was produced by the Greek mathematician Hipparchus in about 140 BC. Although these tables have not survived, it is claimed that twelve books of tables of chords were written by Hipparchus. This makes Hipparchus the founder of trigonometry.

Why is it called mensuration? ›

The term menstruation originated from the Latin word mensis, which means month, and the Greek word mene, which refers to the moon. In ancient times, the menstrual cycle was thought to be related to the moon's cycle because both cycles last around 29 days.

How many 2D shapes are there? ›

The basic types of 2d shapes are a circle, triangle, square, rectangle, pentagon, quadrilateral, hexagon, octagon, etc. Apart from the circle, all the shapes are considered as polygons, which have sides. A polygon which has all the sides and angles as equal is called a regular polygon.

What is mensuration in 10th class? ›

Mensuration formulas for class 10 mainly include formulas involving the volume and surface area of standard 2D and 3D shapes. Here, the list of some important class 10 mensuration formulas is given for the students to skim through them and retain them for longer quickly.

What is pi and its value? ›

In decimal form, the value of pi is approximately 3.14. But pi is an irrational number, meaning that its decimal form neither ends (like 1/4 = 0.25) nor becomes repetitive (like 1/6 = 0.166666...). (To only 18 decimal places, pi is 3.141592653589793238.)

What is the conclusion of mensuration? ›

Answer: Without mensuration, it'll be nearly impossible to construct buildings perfectly with minimum wastage of material . Also, mensuration is probably used in industries to find out the amount of material needed to produce a given number of objects.

Why is area of equilateral triangle? ›

In an equilateral triangle, median, angle bisector and altitude for all sides are all the same and are the lines of symmetry of the equilateral triangle. The area of an equilateral triangle is √3 a2/ 4. The perimeter of an equilateral triangle is 3a.

What is a formula of perimeter of circle? ›

As we know, the circumference (or) perimeter of a circle = 2πr units. The area of a circle = πr2 square units. Now, substitute the values in the perimeter and area of circle formula, we get. The area of circle = πr2 = 3.14(5)2. A = 3.14(25)

What is the perimeter of all shapes? ›

A perimeter means the distance of the boundary of a two-dimensional shape. Also, it is defined as the sum of the length of all the sides of the object. The algebraic sum of the length of each side is the perimeter of that shape. We have formulas available for the various shapes in geometry.

What is the formula of inverse proportion Class 8? ›

The formula of inverse proportion is y = k/x, where x and y are two quantities in inverse proportion and k is the constant of proportionality.

What is math full form? ›

The meaning or full form of MATH is "Mathematics".

What are the top 5 formulas in math? ›

Algebra
  • Completing the square: x2+bx+c=(x+b2)2−b24+c.
  • Quadratic formula: the roots of ax2+bx+c are −b±√b2−4ac2a.
  • Circle: circumference=2πr, area=πr2.
  • Sphere: vol=4πr3/3, surface area=4πr2.
  • Cylinder: vol=πr2h, lateral area=2πrh, total surface area=2πrh+2πr2.

Who invented maths? ›

But Archimedes is known as the father of mathematics.

What is a formula for a rectangle? ›

The formula for the Area of a Rectangle. Area of a Rectangle. A = l × b. The area of any rectangle is calculated, once its length and width are known. By multiplying length and breadth, the rectangle's area will obtain in a square-unit dimension.

What is side formula? ›

Therefore, the side angle side formula or the area of the triangle using the SAS formula = 1/2 × a × b × sin c. Let us work on some problems to understand the side angle side formula. Break down tough concepts through simple visuals.

What's the square of 15? ›

This is Expert Verified Answer

The Square of 15 is 225.

What is circle and its formula? ›

Formulas Related to Circles
Diameter of a CircleD = 2 × r
Circumference of a CircleC = 2 × π × r
Area of a CircleA = π × r2

What is 3D mensuration? ›

Mensuration 3D deals with shapes like cube, cuboid, sphere etc. The problems are generally based on volume and surface area.

What is mensuration 2D? ›

Mensuration 2D mainly deals with problems on perimeter and area. The shape is two dimensional, such as triangle, square, rectangle, circle, parallelogram, etc. This topic does not has many variations and most of the questions are based on certain fixed formulas.

What are the types of mensuration? ›

  • There are two types of Mensuration: 2D Mensuration and 3D Mensuration.
  • The 2D figures have only two diMensions, which are primarily length and width. There is no height or depth to the two-diMensional figure. ...
  • The three diMensions of 3D figures are length, breadth, and height or depth.

Which topics comes under mensuration? ›

Mensuration refers to the branch of mathematics which involves the study of various geometrical shapes.
...
Mensuration
  • Cylinder.
  • Circles.
  • Polygons.
  • Rectangles and Squares.
  • Trapezium, Parallelogram and Rhombus.
  • Area and Perimeter.
  • Cube and Cuboid.

What is the cube formula? ›

Length = Breadth = Height = a. Thus, the measure of each edge of the cube = a. Therefore, the volume of cube formula is a × a × a = a3. It is to be noted that the number obtained using cube formula is the perfect cube number.

Who is the father of mensuration? ›

Archimedes is the father of mensuration. Q. 4.

How many 3D shapes are there? ›

What are the different types of three dimensional shapes? The different types of three dimensional shapes are cone, cylinder, cuboid, cube, sphere, rectangular prism, pyramid.

How many 2D shapes are there? ›

The basic types of 2d shapes are a circle, triangle, square, rectangle, pentagon, quadrilateral, hexagon, octagon, etc. Apart from the circle, all the shapes are considered as polygons, which have sides. A polygon which has all the sides and angles as equal is called a regular polygon.

What is pi and its value? ›

In decimal form, the value of pi is approximately 3.14. But pi is an irrational number, meaning that its decimal form neither ends (like 1/4 = 0.25) nor becomes repetitive (like 1/6 = 0.166666...). (To only 18 decimal places, pi is 3.141592653589793238.)

What are the formulas of mensuration Class 8? ›

Mensuration Class 8 Formulas
Area of Trapeziumheight x (sum of parallel sides)/2
Surface area of cylinder2πr(r + h)
Volume of Cuboidl × b × h
Volume of Cubea3
Volume of cylinderπr2h
4 more rows
19 Feb 2021

Who is the father of maths? ›

Who is Archimedes? The Father of Math is the great Greek mathematician and philosopher Archimedes.

Why do we study mensuration? ›

Uses of Mensuration

Measurement of agricultural fields, floor areas required for purchase/selling transactions. Measurement of volumes required for packaging milk, liquids, solid edible food items. Measurements of surface areas required for estimation of painting houses, buildings, etc.

Why area of square is a2? ›

Why is the area of a square a side square? A square is a 2D figure in which all the sides are of equal measure. Since all the sides are equal, the area would be length times width, which is equal to side × side. Hence, the area of a square is side square.

What is diagonal formula? ›

Number of Diagonals = n(n-3)/2

In other words, an n-sided polygon has n-vertices which can be joined with each other in nC2 ways. Now by subtracting n with nC2 ways, the formula obtained is n(n-3)/2. For example, in a hexagon, the total sides are 6.

What is called mensuration? ›

Definition of mensuration

1 : the act of measuring : measurement. 2 : geometry applied to the computation of lengths, areas, or volumes from given dimensions or angles.

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