Revision: Mensuration Maths Secondary School (English Medium) (5 to 8) Class 8 CBSE

• Dimension: Dimensions in mathematics are the measure of the size or distance of an object or region or space in one direction. In simpler terms, it is the measurement of the length, width, and height of anything.
• Zero-dimensional: A point is a zero-dimensional object as it has no length, width, or height. It has no size. It tells about the location only. A point is dimensionless.
• One Dimensional: A line segment drawn on a surface is a one-dimensional object, as it has only length and no width.
• The 2-dimensional shapes or Plane Figures: The 2-dimensional shapes or objects in geometry are flat plane figures that have two dimensions – length and width.
• The 3-dimensional shapes or solid object: A solid object has three measurements like length, breadth, height, or depth. Hence, they are called three-dimensional shapes. Also, a solid object occupies some space

• Cube: A cube is a three-dimensional solid object bounded by six square faces, facets, or sides, with three meetings at each vertex. The cube is the only regular hexahedron (i.e., a solid figure with six plane faces) and is one of the five Platonic solids. It has 6 faces, 12 edges, and 8 vertices.
• Lateral surface area of the cube: Out of the six faces of a cube, we only find the area of the four faces, leaving the bottom and top faces. In such a case, the area of these four faces is called the lateral surface area of the cube.

A cylinder is a three-dimensional solid figure that has two identical circular bases joined by a curved surface at a  particular distance from its centre, which is its height.

Area of the trapezium = `1/2` × sum of the lengths of parallel sides × height.

Area of quadrilateral = `1/2` d (height₁ + height₂) where d denotes the length of diagonal.

• Area of a rhombus = `1/2` x product of lengths of diagonals.

• Total surface area of cuboid = 2(lb + bh + lh)
• The lateral surface area of a cuboid = 2h(l + b)

• Cuboid: A cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube. A cuboid looks like a rectangular box. It has 6 faces. Each face has 4 edges. Each face has 4 corners (called vertices).
• Surface of a cuboid: the outer surface of a cuboid is made up of six rectangles (in fact, rectangular regions, called the faces of the cuboid), whose areas can be found by multiplying the length by breadth for each of them separately and then adding the six areas together.
• Lateral surface area of the cuboid: Out of the six faces of a cuboid, we only find the area of the four faces, leaving the bottom and top faces. In such a case, the area of these four faces is called the lateral surface area of the cuboid.

• Total surface area of the cube = 6a².
• Lateral surface area of a cube = 4a².

Curved surface area of a cylinder = circumference of base × height

                                                        = 2πrh

Total surface area = Curved surface area + 2 (Area of cross-section)

                               = 2πrh + 2πr²

                               = 2πr(r + h)

Volume = Area of cross-section × height (or, length)

              = πr²h

Cylinder + Two Hemispheres

TSA = CSA of cylinder + 2 × CSA of hemisphere

Cone + Hemisphere

TSA = CSA of cone + CSA of hemisphere

Cube + Hemisphere

TSA = TSA of cube − area of circular base + CSA of hemisphere

• Volume of a Cuboid = l × b × h

• Volume of cube = l³.