1 गोला (sphere)
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Volume (आयतन): (V) = 4/3* πr3
- Surface Area(पृष्ठीय क्षेत्रफल): A = 4πr²
- Diameter (व्यास): d = 2r
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Circumference(वक्र पृष्ठीय): C = 2πr
2 CYLINDER (बेलन)
Cylinder Formulas (बेलन के सूत्र)
- r = Radius of the cylinder base (बेलन के आधार की त्रिज्या)
- h = Height of the cylinder (बेलन की ऊँचाई)
- π = Pi ( 3.14 ,(22\7))
1. Volume of a Cylinder (बेलन का आयतन)
The amount of 3-dimensional space enclosed by the cylinder.
: V = πr²h
2. Curved Surface Area / Lateral Surface Area (वक्र पृष्ठीय क्षेत्रफल / पार्श्व पृष्ठीय क्षेत्रफल)
The area of the curved sides only (excluding the top and bottom circles).
- CSA = 2πrh
3. Total Surface Area (कुल पृष्ठीय क्षेत्रफल / संपूर्ण पृष्ठीय क्षेत्रफल)
The area of the curved side plus the areas of the top and bottom circular bases.
TSA = 2πr(r + h)
3 cone (शंकु)
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Cone Formulas (शंकु के सूत्र)
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Radius (r): Base radius
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Height (h): Vertical height of the cone
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Slant Height (l): =√(r²+ℎ²)
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CSA (Curved Surface Area): πrl
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TSA (Total Surface Area): = π r (r + l)
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4 FRUSTUM (छिन्नक)
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Slant Height (): =√ℎ²+(R-r)²
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Curved Surface Area (CSA): π(R + r)l
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Total Surface Area (TSA): TSA = π(R + r)l + π R² + π r²
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Volume 1/3πℎ(R²+r²+Rr)
- 5 CUBE & CUBOID
Cube (घन)
A cube has 6 equal square faces with side a
- Volume (आयतन): a³
- Total Surface Area (कुल पृष्ठीय क्षेत्रफल): 6a² , 6 × square of sides
- Lateral Surface Area (पार्श्व पृष्ठीय क्षेत्रफल): 4a²
- Diagonal (विकर्ण): a√3
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Perimeter (परिमाप): 12a
Cuboid (घनाभ)
A cuboid is a 3D box with 6 rectangular faces.
- Volume (आयतन): (L×B×H) here L is lenght , B is width , H is height
- Total Surface Area (कुल पृष्ठीय क्षेत्रफल): (2(lb + bh + hl))
- Lateral Surface Area / Area of 4 walls (पार्श्व पृष्ठीय क्षेत्रफल): (2h(l + b))
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Diagonal (विकर्ण): √(L²+B²+H²)
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Perimeter (परिमाप): 4(l + b + h)
6 PYRAMID
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Volume: (V = 1/3 × area of Base × height )
- Lateral Surface Area (LSA): (LSA = 1/2 ×Perimeter of the base ×Slant height )
- Total Surface Area (TSA): (TSA = B + 1/2×P×l)
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Slant Height (l): = √(h²+r²)
- B = Area of the base (dependent on base shape, e.g., length × width for a rectangle)
- h = Perpendicular height (vertical distance from the apex to the center of the base)
- P = Perimeter of the base
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l = Slant height (the height of the triangular side faces)
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7 HEXAGONE
Angles and Diagonals
- Interior Angle: Each interior angle is (120°)
- Exterior Angle: Each exterior angle is (60°)
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Number of Diagonals: 9
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Area Formula
- Using side length : (A = 6 × √3/4 × a²
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Using apothem (a): (A = 1/2 × perimeter × a
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Perimeter Formula = 6 × a
The perimeter of a regular hexagon is the total length of its outer boundary