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NCERT Class 8 Mathematics Chapter 11 Mensuration CBSE Board Sample Problems
Mensuration
Sr. no | Term | Description |
1. | Mensuration | It is branch of mathematics which is concerned about the measurement of length, area and Volume of plane and solid figure. |
2. | Perimeter | The perimeter of plane figure is defined as the length of the boundary It units is same as that of length i.e.. m, cm, km |
3. | Area | The area of the plane figure is the surface enclosed by its boundary It unit is square of length unit. i.e.. |
Shapes Where Area and Perimeter Are Known
Shapes | perimeter | Area |
Rectangle | P = 2 (L + B) L and B are Length and Breadth of the rectangle | |
Square | P = 4 a A is side of the square | |
Triangle | P = sum of sides | |
Parallelogram | P = 2 (sum of adjacent sides) | |
Circle | r is the radius of the circle | |
Trapezium | P = sum of length of all the sides | Half the product of the sum of the lengths of parallel sides and the perpendicular distance between them gives the area of trapezium |
General Quadrilaterals | P = sum of length of all the sides | |
Rhombus | P = 4 a | Where d1 and d2 are the diagonals of the Rhombus. |
Important Terms to remember in case of solid figures
Surface Area | Surface Area of a solid is the sum of the areas of its faces |
Lateral Surface Area | The faces excluding the top and bottom make the later Surface Area of the solid |
Volume | Amount of space occupied by a three dimensional object (solid figure) is called its volume. We use square units to find the area of a two dimensional region. In case of volume we will use cubic unit to find the volume of a solid, as cube is the most convenient solid shape (just as square is the most convenient shape to measure area of a region) Volume is sometimes refer s capacity also |
Surface Area and Volume of Cube and Cuboid
Type | Measurement |
Surface area of cuboid of length L, Breadth B and Height H | |
Lateral Surface Area of the cuboids | |
Diagonal of the cuboids | |
Volume of a cuboids | LBH |
Length of all 12 edges of the cuboids | |
Surface Area of cube of side L | |
Lateral Surface Area of the cube | |
Diagonal of the cube | |
Volume of a cube |
Surface Area and volume of Right circular cylinder
Radius | The radius (r) of the circular base is called the radius of the cylinder |
Height | The length of the axis of the cylinder is called the height (h) of the cylinder |
Lateral surface | The curved surface joining the two base of a right circular cylinder is called lateral surface. |
Type | Measurement |
Curved or lateral Surface Area of cylinder | |
Total Surface Area of cylinder | |
Volume of cylinder |