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MENSURATION – CYLINDER, CONE, SPHERE

MENSURATION – CYLINDER, CONE, SPHERE

Menstruation is the branch of mathematics which deals with the study of Geometric shapes, their area, volume and related parameters.

Some important menstruation formulas are:

  1. Area of rectangle (A) = length (l) × Breath(b)

 A=l X b

  1. Perimeter of a rectangle (P) = 2 × (Length(l) + Breath(b))

P = 2 X (l + b)

  1. Area of a square (A) = Length (l) × Length (l)

A = l X l

  1. Perimeter of a square (P) = 4 × Length (l)

P = 4 X l

  1. Area of a parallelogram (A) = Length (l) × Height (h)

A = l X h

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  1. Perimeter of a parallelogram (P) = 2 × (length (l) + Breadth(b))

P = 2 X (l + b)

  1. Area of a triangle (A) = (Base (b) × Height (b)) / 2

A = ½ X b X h

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And for a triangle with sides measuring “a”, “b” and “c”, Perimeter = a + b + c

And s = semi perimeter = perimeter / 2 = (a + b + c)/2

And also: Area of triangle

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This formula is also known as “Heron’s formula”.

 8. Area of triangle (A) =

  9

 

Where A, B and C are the vertex and angle A , B , C are respective angles of triangles and  a , b , c are the respective

opposite sides of the angles as shown in figure below:

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Area of triangle – mensuration

 

  1. Area of isosceles triangle =

 11

 Where a = length of two equal side, b= length of base of isosceles triangle.

10. Area of trapezium (A) =

12

 

 

Where “a” and “b” are the length of parallel sides and “h” is the perpendicular distance between “a” and “b”

11. Perimeter of a trapezium (P) = sum of all sides

 

  1. Area of rhombus (A) = Product of diagonals / 2

 

  1. Perimeter of a rhombus (P) = 4 × l

Where l = length of a side

 

  1. Area of quadrilateral (A) = 1/2 × Diagonal × (Sum of offsets)

 

  1. Area of a Kite (A) = 1/2 × product of its diagonals

 

  1. Perimeter of a Kite (A) = 2 × Sum on non-adjacent sides

 

  1. Area of a Circle (A)

Where r = radius of the circle and d = diameter of the circle.

 

  1. Circumference of a Circle =

r= radius of circle

d= diameter of circle

 

  1. Total surface area of cuboid =

Where l= length, b=breadth, h=height

 

  1. Total surface area of cuboid = 6

Where l= length

 

  1. Length of diagonal of cuboid =

 

  1. Length of diagonal of cube =

 

  1. Volume of cuboid = l × b × h

 

  1. Volume of cube = l × l × l

 

  1. Area of base of a cone =

 

  1. Curved surface area of a cone = C =

Where r = radius of base, l = slanting height of cone

 

  1. Total surface area of a cone =

 

  1. Volume of right circular cone =

Where r = radius of base of cone, h= height of the cone (perpendicular to base)

 

  1. Surface area of triangular prism = (P × height) + (2 × area of triangle)

Where p = perimeter of base

 

  1. Surface area of polygonal prism = (Perimeter of base × height) + (Area of polygonal base × 2)

 

  1. Lateral surface area of prism = Perimeter of base × height

 

  1. Volume of Triangular prism = Area of the triangular base × height

 

  1. Curved surface area of a cylinder =

Where r = radius of base, h = height of cylinder

 

  1. Total surface area of a cylinder =
  2. Volume of a cylinder =

 

  1. Surface area of sphere =

Where r= radius of sphere, d= diameter of sphere

 

  1. Volume of a sphere =
  2. Volume of hollow cylinder =

Where, R = radius of cylinder, r= radius of hollow, h = height of cylinder

 

  1. Right Square Pyramid:

If a = length of base, b= length of equal side; of the isosceles triangle forming the slanting face, as shown in figure:

Net diagram of right square pyramid

  1. A Surface area of a right square pyramid =
  2. B Volume of a right square pyramid =

 

 

  1. Square Pyramid:
  2. a. Johnson Pyramid:

Net diagram of Johnson pyramid

Volume = (
Total Surface Area:

  1. b. Normal Square pyramid:

If a = length of square base and h = height of the pyramid then:
Volume =

Total Surface Area =

  1. Area of a regular hexagon =
  2. Area of equilateral triangle =
  3. Curved surface area of a Frustums =
  4. Total surface area of a Frustums =
  5. Curved surface area of a Hemisphere =
  6. Total surface area of a Hemisphere =
  7. Volume of a Hemisphere =
  8. Area of sector of a circle =

Where  = measure of angle of the sector, r= radius of the sector