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Mathematics Class 8 - Mensuration Notes

Comprehensive study notes for Class 8 - Mensuration olympiad preparation

Mensuration

Welcome to the chapter on Mensuration for Class 8. In this chapter, you will learn how to measure and calculate the perimeter, area, and volume of different shapes. By the end of this chapter, you will be able to solve problems related to 2D and 3D figures confidently!

Introduction

Mensuration is the branch of mathematics that deals with measuring lengths, areas, and volumes of different shapes and objects. It helps us find out how much space a shape covers or how much it can hold.

Perimeter

The perimeter is the total length of the boundary of a closed figure.

  • Rectangle: Perimeter = 2 × (length + breadth)
  • Square: Perimeter = 4 × side
  • Triangle: Perimeter = sum of all sides

Area

Area is the amount of surface a shape covers.

  • Rectangle: Area = length × breadth
  • Square: Area = side × side
  • Triangle: Area = ½ × base × height
  • Circle: Area = π × radius × radius

Surface Area and Volume

Surface area is the total area of all the faces of a 3D object. Volume is the amount of space inside a 3D object.

  • Cuboid: Surface Area = 2(lb + bh + hl), Volume = length × breadth × height
  • Cube: Surface Area = 6 × side × side, Volume = side × side × side
  • Cylinder: Surface Area = 2πr(h + r), Volume = π × r × r × h
  • Sphere: Surface Area = 4πr², Volume = (4/3)πr³

Units of Measurement

  • Length: millimeter (mm), centimeter (cm), meter (m), kilometer (km)
  • Area: square centimeter (cm²), square meter (m²)
  • Volume: cubic centimeter (cm³), cubic meter (m³), liter (L)

Word Problems

Use mensuration formulas to solve real-life problems. Read the question, identify the shape, and apply the correct formula.

  • Example: Find the area of a rectangle with length 12 cm and breadth 8 cm. (Area = 12 × 8 = 96 cm²)
  • Example: Find the volume of a cube with side 5 cm. (Volume = 5 × 5 × 5 = 125 cm³)

Fun Activity: Measure and Calculate!

Use a ruler to measure the sides of your notebook. Calculate its perimeter and area!

Summary

  • Mensuration helps us measure perimeter, area, and volume.
  • Use the correct formula for each shape.
  • Practice solving word problems for real-life applications.

Practice Questions

  1. Find the perimeter of a square with side 7 cm.
  2. Find the area of a rectangle with length 15 cm and breadth 10 cm.
  3. Find the volume of a cuboid with length 6 cm, breadth 4 cm, and height 5 cm.
  4. Find the surface area of a cube with side 3 cm.
  5. Find the area of a triangle with base 8 cm and height 5 cm.

Challenge Yourself

  • Make your own word problem using area and perimeter.
  • Find the volume of a cylinder with radius 3 cm and height 7 cm.

Did You Know?

  • The value of π (pi) is about 3.14.
  • Mensuration is used in architecture, engineering, and daily life!

Glossary

  • Perimeter: The total length around a shape.
  • Area: The surface covered by a shape.
  • Volume: The space inside a 3D object.
  • Surface Area: The total area of all faces of a 3D object.

Answers to Practice Questions

  1. 28 cm
  2. 150 cm²
  3. 120 cm³
  4. 54 cm²
  5. 20 cm²

Practice mensuration every day to become confident in measuring shapes and solving problems!

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