Solids

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A solid is anything which occupies space and has a definite shape. Key characteristics: (1) It has three dimensions - length, breadth, and height (2) It is a three-dimensional (3-D) figure (3) It occu…

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Volume is the space occupied by a solid. For hollow bodies: (a) Capacity of a container = Its internal volume (b) Volume of material in a hollow body = External volume - Internal volume. Example: A wo…

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The surface area of a solid is the sum of the areas of all the surfaces of the solid. It is also called the total surface area. It represents the total area that would need to be painted or covered if…

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Volume of a cuboid = length × breadth × height = l × b × h. This formula gives the amount of space inside the cuboid. Units are cubic units (cm³, m³, etc.).

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Total surface area of cuboid = 2(l×b + b×h + h×l). This represents the sum of areas of all 6 faces: 2 faces each of dimensions l×b, b×h, and h×l. The factor 2 accounts for opposite faces being equal.

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Lateral surface area of a cuboid is the sum of areas of the four walls (vertical faces) of the cuboid, excluding the top and bottom faces. Formula: Lateral surface area = 2(l + b) × h. It's useful whe…

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Diagonal of cuboid = √(l² + b² + h²). Derivation: In base rectangle, diagonal = √(l² + b²). This diagonal, height h, and space diagonal form a right triangle. Using Pythagoras: (space diagonal)² = (√(…

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For a cube with edge = a: (1) Volume = a³ (2) Total surface area = 6a² (3) Lateral surface area = 4a² (4) Diagonal = a√3. Note: A cube is a special cuboid where l = b = h = a.