**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:

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

*A=l X b*

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

*P = 2 X (l + b)*

- Area of a square (A) = Length (l) × Length (l)

*A = l X l*

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

*P = 4 X l*

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

*A = l X h*

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

P = 2 X (l + b)

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

A = ½ X b X h

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

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

8. Area of triangle (A) =

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:

Area of triangle – mensuration

- Area of isosceles triangle =

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

10. Area of trapezium (A) =

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

- Area of rhombus (A) = Product of diagonals / 2

- Perimeter of a rhombus (P) = 4 × l

Where l = length of a side

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

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

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

- Area of a Circle (A)

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

- Circumference of a Circle =

r= radius of circle

d= diameter of circle

- Total surface area of cuboid =

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

- Total surface area of cuboid = 6

Where l= length

- Length of diagonal of cuboid =

- Length of diagonal of cube =

- Volume of cuboid =
*l × b × h*

- Volume of cube
*= l × l × l*

- Area of base of a cone =

- Curved surface area of a cone = C =

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

- Total surface area of a cone =

- Volume of right circular cone =

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

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

Where p = perimeter of base

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

- Lateral surface area of prism = Perimeter of base × height

- Volume of Triangular prism = Area of the triangular base × height

- Curved surface area of a cylinder =

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

- Total surface area of a cylinder =
- Volume of a cylinder =

- Surface area of sphere =

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

- Volume of a sphere =
- Volume of hollow cylinder =

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

- 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

- A Surface area of a right square pyramid =
- B Volume of a right square pyramid =

- Square Pyramid:
- a. Johnson Pyramid:

Net diagram of Johnson pyramid

Volume = (

Total Surface Area:

- b. Normal Square pyramid:

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

Volume =

Total Surface Area =

- Area of a regular hexagon =
- Area of equilateral triangle =
- Curved surface area of a Frustums =
- Total surface area of a Frustums =
- Curved surface area of a Hemisphere =
- Total surface area of a Hemisphere =
- Volume of a Hemisphere =
- Area of sector of a circle =

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