Mensuration
Overview
Mensuration is the branch of mathematics that deals with the measurement of geometric figures and their parameters like length, area, and volume. In Class 8, students learn to find areas of plane figures like trapezium, rhombus, and polygons, and extend their understanding to 3D shapes such as cubes, cuboids, cylinders, and cones, calculating their surface areas and volumes using standard formulas.
Typed Notes
Areas of Plane Figures
A trapezium has one pair of parallel sides. Its area is calculated as half the product of the sum of parallel sides and the perpendicular height between them. A rhombus is a quadrilateral with all sides equal; its area equals half the product of its two diagonals. For general polygons, we divide the shape into triangles or trapeziums and add their individual areas. These formulas help solve real-life problems like finding the area of fields or floor designs.
Surface Area of 3D Shapes
Surface area is the total area of all outer faces of a solid. For a cuboid with length l, breadth b, and height h, Total Surface Area = 2(lb + bh + hl) and Lateral Surface Area = 2h(l + b). For a cube of side a, TSA = 6a². For a cylinder of radius r and height h, Curved Surface Area = 2πrh and Total Surface Area = 2πr(r + h). These are used in packaging, painting walls, and manufacturing containers.
Volume of 3D Shapes
Volume measures the space occupied by a solid. Volume of a cuboid = l × b × h. Volume of a cube = a³. Volume of a cylinder = πr²h. The standard unit of volume is cm³ or m³. Capacity is the volume of liquid a container can hold, measured in litres (1 litre = 1000 cm³). For example, a water tank's capacity is found using the cylinder formula. Understanding volume helps in everyday tasks like filling tanks, packing boxes, and cooking measurements.
Comparing Quantities Using Mensuration
Mensuration connects to real life when we compare costs of painting, tiling, or filling objects. For instance, the cost of painting a wall = Area of wall × Rate per m². The cost of filling a tank = Volume × Rate per litre. When a shape is recasted or melted into another, the volume remains the same. Students must carefully identify which formula to use — surface area for covering problems and volume for filling problems — to avoid common errors in calculation.
Key Concepts
Revision ke liye ek nazar — exam se pehle yahi padhna hai.
- 01Area of a trapezium = ½ × (sum of parallel sides) × height
- 02Area of a rhombus = ½ × d1 × d2, where d1 and d2 are diagonals
- 03Total Surface Area of a cuboid = 2(lb + bh + hl); Volume = l × b × h
- 04Curved Surface Area of a cylinder = 2πrh; Total SA = 2πr(r + h); Volume = πr²h
- 05Volume of a cube = a³; Total Surface Area of a cube = 6a²
Important Formulas
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
Find the area of a trapezium whose parallel sides are 10 cm and 6 cm, and the height is 8 cm.
Find the area of a rhombus whose diagonals are 12 cm and 9 cm.
Find the Total Surface Area of a cuboid with length 8 cm, breadth 5 cm, and height 3 cm.
A cylindrical tank has radius 7 cm and height 20 cm. Find its volume. (Use π = 22/7)
Find the Total Surface Area of a cube whose side is 6 cm.
Mensuration in Class 8 covers area of trapezium and rhombus, and surface area and volume of cuboids, cubes, and cylinders. Area formulas deal with flat surfaces while surface area covers all faces of 3D solids. Volume measures space inside a solid. Key formulas include Area of trapezium = ½(a+b)h, Volume of cylinder = πr²h, and TSA of cuboid = 2(lb+bh+hl). These concepts are widely used in real-life applications.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.What is the formula for the area of a trapezium with parallel sides a and b, and height h?
Q2.A cube has side 4 cm. What is its volume?
Q3.Which formula gives the Curved Surface Area of a cylinder?
Q4.The diagonals of a rhombus are 16 cm and 10 cm. What is its area?
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