கணிதம் உங்களுக்காக - 12 - கான்ஸெப்ட்கள்

 1. Volume of a frustum of a cone: V = (1/3)πh(R₁² + R₁R₂ + R₂²) (where h is the height, R₁ is the radius of the top base, and R₂ is the radius of the bottom base)

2. Surface area of a frustum of a cone: SA = π(R₁ + R₂)√((R₁ - R₂)² + h²) + πR₁² + πR₂²

3. Volume of a frustum of a pyramid: V = (1/3)h(A₁ + A₂ + √(A₁A₂)) (where h is the height, A₁ is the area of the top base, and A₂ is the area of the bottom base)

4. Surface area of a frustum of a pyramid: SA = A₁ + A₂ + (1/2)Pℓ (where P is the perimeter of the base and ℓ is the slant height)

5. Volume of a regular dodecahedron: V = (15 + 7√5) / 4 a³ (where a is the side length)

6. Surface area of a regular dodecahedron: SA = 3√25 + 10√5 a² (where a is the side length)

7. Volume of a regular icosahedron: V = 5(3 + √5) / 12 a³ (where a is the side length)

8. Surface area of a regular icosahedron: SA = 5√3 a² (where a is the side length)

9. Polar to Cartesian coordinates: x = r cos(θ), y = r sin(θ)

10. Cartesian to Polar coordinates: r = √(x² + y²), θ = tan⁻¹(y / x)

11. Equation of a circle in polar coordinates: r(θ) = R (where R is the radius)

12. Equation of a line in polar coordinates: r(θ) = (l) / (cos(θ - φ)) (where l is the perpendicular distance from the origin and φ is the angle with the positive x-axis)

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13. Power of a Point Theorem: If a point P lies outside a circle and two secant lines PA and PB intersect the circle at A and B, then PA × PB = PC × PD (where C and D are points of intersection)

14. Segment lengths in a circle: If two chords AB and CD intersect at point P inside the circle, then PA × PB = PC × PD.

15. Length of a tangent segment: If a tangent from an external point P touches the circle at T, then PT² = PA × PB (where A and B are points of intersection of a secant through P)

16. Length of an arc: L = rθ (where r is the radius and θ is the central angle in radians)

17. Area of a sector: A = 1/2r²θ (where r is the radius and θ is the central angle in radians)

18. Segment area: A = 1/2r²(θ - sinθ)

19. Length of a median of a triangle: m = 1/2 √(2b² + 2c² - a²) (where a, b, and c are the lengths of the sides of the triangle, and m is the median to side a)

20. Length of an altitude in a triangle: h = 2A / a (where A is the area of the triangle and a is the base)

21. Length of an angle bisector in a triangle: l = √(bc