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Volume Formulas for All 3D Shapes

Volume measures the space a 3D shape occupies, expressed in cubic units (cm³, m³, in³). Each shape has its own formula - cube uses V = a³, cuboid uses l × b × h, cylinder uses πr²h, sphere uses ⁴⁄₃ πr³, and cones and pyramids hold exactly one-third of their corresponding cylinder or prism.

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Slope Formula: How to Find the Slope of a Line

The slope formula is m = (y₂ − y₁) / (x₂ − x₁) - it calculates the steepness and direction of a line from any two points on it. Slope can be positive (line rises), negative (line falls), zero (horizontal), or undefined (vertical). The formula is also written as rise over run, where rise = Δy and run = Δx.

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Distance Formula in Maths: Definition, Derivation, and Examples

The distance formula, d = √[(x₂ − x₁)² + (y₂ − y₁)²], gives the straight-line distance between two points on a coordinate plane. It is derived from the Pythagorean theorem and extends to 3D by adding a z-coordinate term.

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Geometry Formulas: Area, Perimeter & Volume for 2D and 3D Shapes

Geometry formulas calculate the perimeter and area of 2D shapes (square, rectangle, triangle, circle) and the surface area and volume of 3D shapes (cube, cuboid, cylinder, cone, sphere). Perimeter uses linear units (cm), area and surface area use square units (cm²), and volume uses cubic units (cm³).

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Integration Formulas: Complete List with Examples

Integration formulas are the standard antiderivative results used to solve integrals across Class 11, 12, and JEE - covering basic, trigonometric, inverse trigonometric, exponential, logarithmic, hyperbolic, and special integrals. The general form is ∫f'(x) dx = f(x) + C.

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