Mensuration

# Mensuration

Mensuration is the branch of mathematics that studies measurements of various geometrical figures and their basic parameters like length, area, volume and more. The article below discusses the basic concept of mensuration and all the measurement formulas.

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## Mensuration Maths Definition

The branch of mathematics that studies measurements of various geometrical figures and their basic parameters like length, area, volume, etc, is called Mensuration.

These shapes exist either as 2D figures or 3D figures.

## Mensuration Class 8: Difference Between 2D and 3D Figures

Below given table gives us the difference between 2D and 3D shapes.

 Aspect 2D Shapes 3D Shapes Dimension It exists in 2 dimensions. It exists in 3 dimensions. Examples Square, triangle, circle Cube, cone, sphere. Representation It is Flat and can be drawn on a plane These are Solid and occupy space Properties The area is the main property Volume and surface area are the main properties Measurements Length and area Length, area, and volume Visual representation They appear as flat shapes on paper They appear as solid objects in space Real-world applications Measuring floor area, drawing shapes, calculating perimeters, etc. Measuring volumes, designing buildings, creating 3D models, etc.

## Mensuration Formulas: Important Terms Related to Mensuration in Maths

Let’s have a look at important terms related to Mensuration in Mathematics.

 Terms Abbreviation Unit Definition Area A m² or cm² A closed shape covers the surface. Perimeter P cm or m Measures the continuous line along the boundary of a figure. Volume V cm³ or m³ A 3D shape occupies the space. Curved Surface Area CSA m² or cm² The total area of a curved surface in a 3D shape (e.g., Sphere). Lateral Surface Area LSA m² or cm² The total area of all lateral surfaces surrounding a 3D figure. Total Surface Area TSA m² or cm² The sum of curved and lateral surface areas of a 3D shape. Square Unit – m² or cm² The area is covered by a square of one unit side length. Cube Unit – m³ or cm³ The volume occupied by a cube with one side of one unit length.

## Mensuration Formulas

Mensuration in mathematics is the study of measurements of various geometrical figures and their basic parameters like length, area, volume, etc. Therefore, let’s look at the formulas of mensuration related to 2D and 3D shapes. One must have the formula list with him as it makes it easy for students to learn and solve the mathematical problems.

### Mensuration All Formulas for 2D Shapes:

Below mentioned tables consists of most commonly used Mensuration Formulas in 2D geometry.

 Shape Area (Square Units) Perimeter (Units) Square a² 4a Rectangle l × b 2(l + b) Circle πr² 2πr Scalene Triangle √[s(s−a)(s−b)(s−c)], Where, s = (a+b+c)/2 a + b + c Isosceles Triangle ½ × b × h 2a + b Equilateral Triangle (√3/4) × a² 3a Right Angle Triangle ½ × b × h b + hypotenuse + h Rhombus ½ × d₁ × d₂ 4 × side Parallelogram b × h 2(l + b) Trapezium ½ × h(a + c) a + b + c + d

### Mensuration All Formulas for 3D Shapes:

Below mentioned tables consists of most commonly used Mensuration Formulas in 3D geometry.

 Shape Volume (Cubic Units) Curved or Lateral Surface Area Total Surface Area (TSA) (Square Units) Cube a³ CSA = 4a² 6a² Cuboid l × b × h LSA = 2h(l + b) 2(lb + bh + hl) Sphere (4/3)πr³ CSA = 4πr² 4πr² Hemisphere (⅔)πr³ LSA = 2πr² 3πr² Cylinder πr²h LSA = 2πrh 2πrh + 2πr² Cone (⅓)πr²h πrl πr(r + l)

## Mensuration Formulas Class 8: Solved Examples

1. Find the area of a rectangle whose length and breadth are 10 cm and 5 cm, respectively.

Ans. Given:

Length of the rectangle = 10 cm

Breadth of the rectangle = 5 cm

Area of the rectangle = length × breadth

Area = 10 cm × 5 cm

= 50 cm²

2. A cylinder has a height of 10 cm and a base radius of 2 cm. Calculate volume and total surface area of this cylinder.

Ans. Given:

Height of the cylinder = 10 cm

The base radius of the cylinder = 2 cm

The volume of the cylinder = πr²h cm cube

Volume = 3.14 × 2² × 10

= 125.6 cm cube

Total Surface Area of the cylinder = 2πrh + 2πr² cm2

TSA = 2 × 3.14 × 2 × 10 + 2 × 3.14 × 2²

= 125.6 + 25.12

= 150.72 cm2

## Mensuration Formulas Class 8: Practice Questions

Ques 1. Find the area and perimeter of a rectangle of length and breadth as 12 cm and 9 cm, respectively.

Ques 2. Find the area and perimeter of a rectangle of length and breadth as 60 cm and 38 cm, respectively.

Ques 3. A cylindrical water tank has a height of 18 m and a base radius of 6 m. Calculate its total surface area.

Ques 4. A cylindrical water tank has a height of 40 m and a base radius of 5 m. Calculate its volume.

Ques 5. A cylindrical water tank has a height of 170 m and a base radius of 20 m. Calculate its volume and total surface area.

## FAQs on Mensuration

### What is mensuration in mathematics?

Mensuration is the branch of mathematics that studies measurements of various geometrical figures and their basic parameters like length, area, volume, etc.

### Name two types of mensuration dimensions

There are 2D and 3D dimensions in Mensuration

### What are mensuration Formulas in maths?

Mensuration in mathematics is the study of measurements of various geometrical figures and their basic parameters like length, area, volume, etc and formulas used respectively are Mensuration Formulas

### Is mensuration in class 10?

Class 10 math covers a bunch of formulas related to measuring things like the space inside and the outer covering of common shapes in 2D and 3D. Here, we've compiled a list of important formulas for class 10 students to easily read and remember for a longer time.

### Who is the father of mensuration?

Leonard Digges is known for advancing the field of Mensuration, but Archimedes is credited with its invention. Mensuration is a branch of math that helps us measure things.

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