# Mensuration Formulas for Class 6 to 10

Mensuration formulas list contains all important mensuration formulas for Class 6 to 10.

By Mohit ChauhanUpdated : Feb 8, 2021 , 2:31 IST Learning mensuration formulas is a challenging task, especially for students who hate Maths. In every class, you will find a complete chapter based on finding the area and perimeter of close plane figures. To define mensuration, it is a branch of geometry in which you need to measure geometrical figures and their parameters, which are as follows.

• Area
• Perimeter
• Volume
• Lateral surface area
• Curved surface area
• Total surface area, etc.

You will come across mensuration formulas of various 2-D and 3-D figures such as square, rectangle, triangle, circle, cuboid, cube, cylinder, sphere, cone, and hemisphere. In this article, you can view mensuration formulas for Classes 6 to 10. Before studying the formulas of mensuration, it is important to understand a few important terminologies related to mensuration.

## Important Terms of Mensuration

To understand and implement geometry in day-to-day applications, you must have a thorough understanding of the important definition of mensuration. We have tabulated the terms and their meanings below.

 Terms Definitions Closed Figures In geometry, a closed figure is defined as an enclosed shape in which all its line segments or curves are connected with each other. Area The region occupied by a two-dimensional close figure is called its area. Perimeter It is the total length of a closed figure along the boundary. Circumference It is the total distance covered when you move around the circular path once along the boundary. Surface Area It is the sum of the areas of faces of a solid figure. Volume The region occupied by a three-dimensional solid figure is called its volume. Frustum of a Cone When a small conical portion from the top of a right circular cone is removed, the resulting solid is called a Frustum of a cone.

### Mensuration Formulas for Class 6

In NCERT Class 6 Maths textbook, you will study the following formulas of mensuration.

 Figure Area Perimeter Rectangle Length x Breadth 2 (length + breadth) Square Side x Side 4 x length of its side Equilateral Triangle ½ x Base x Height 3 x length of a side

### Mensuration Formulas for Class 7

Apart from the three basic mensuration formulas, two additional formulas will come to use when you solve questions of Class 7 Maths NCERT book. Also, go through the common conversions which are given below the table.

 Figure Area Perimeter Rectangle length x breadth 2 (length + breadth) Square side x side 4 x length of its side Equilateral Triangle ½ x base x height 3 x length of a side Parallelogram base x height Total distance along the boundary Circle 𝛑r2 2𝛑r

Conversions

• 1 cm2 = 100 mm2
• 1 m2 = 10000 cm2
• 1 hectare = 10000 m2

### Mensuration Formulas for Class 8

In Class 8, you will study the area and perimeter of trapezium and rhombus. Further, in the mensuration chapter of NCERT Class 8 Maths, you will learn to calculate the total surface area, curved surface area, and volume of closed figures.

 Figure Area Perimeter Trapezium ½ x (sum of the length of the parallel sides) x distance between the parallel sides) Total distance along the boundary Rhombus ½ x product of its diagonals Total distance along the boundary

Total Surface Area, Curved Surface Area and Volume of Closed Figures

Here you can learn to calculate the TSA, LSA/CSA, and volume of closed figures such as cuboid, cylinder, and cube. Also learn the basic conversions that will help you solve NCERT Maths textbook questions easily.

 Figure Total Surface Area Lateral/Curved Surface Area Volume Cuboid 2 (lb + bh + hl) 2(l + b) x h l x b x h Cube 6 x (length)2 4 x (length)2 (length)3 Cylinder 2πr (r + h) 2πrh πr2h

Conversions

• 1 cm3 = 1 ml
• 1 L = 1000 cm3
• 1 m3 = 1000000 cm3 = 1000 L

### Mensuration Formulas for Class 9

In Class 9, you will learn to calculate the TSA, CSA/LSA, and volume of a cone, sphere, and hemisphere.

 Figure Total Surface Area Lateral/Curved Surface Area Volume Cuboid 2 (lb + bh + hl) 2(l + b) x h l x b x h Cube 6 x (length)2 4 x (length)2 (length)3 Cylinder 2πr (r + h) 2πrh πr2h Cone πr (l + r) πrl 1/3πr2h Sphere 4πr2 - 4/3πr3 Hemisphere 3πr2 2πr2 2/3πr3

### Mensuration Formulas for Class 10

The formulae involving the frustum of a cone are as follows.

1. Total surface area of a frustum of a cone = πl (r1 + r2) + π(r12 + r22)

where, h = vertical height of the frustum, l = slant height of the frustum

r1 and r2 are radii of the two bases of the frustum

2. Curved surface area of a frustum of a cone = πl (r1 + r2), where l = √h2 + (r1 - r2)2

3. Volume of a frustum of a cone = 1/3 πh (r12 + r22 + r1r2)

These were all mensuration formulas that you will cover in NCERT textbooks of Classes 6 to 10. You can apply these formulas in a variety of questions related to geometry or revolving around such shapes.

• How to remember mensuration formulas?

Do not try to learn the formulas instead you should understand the derivation of each formula. Also, by breaking a figure into different shapes can help you derive the formula.

• What is the formula of trapezium?

Area of Trapezium= ½ x (sum of the length of the parallel sides) x distance between the parallel sides)

• What is the total surface area of cylinder?

Total Surface Area of Cylinder = 2πr (r + h)

• What is the curved surface area of cone?

Curved Surface Area of Cone = πrl

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