Mensuration (3D) Formulas Tips And Tricks

Mensuration (3D) Formulas Tips And Tricks

It is very important to have an understanding of Different Formulas of quadrilaterals and circle for you to comfortably attempt Advanced Maths questions which covers a major portion of Quant Section of Competitive Exams. Here we are providing you formulas and shortcuts on how to solve mensuration questions.

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Important Mensuration (3D) Formulas

Cube

cube

  • s = side
  • Volume: V = s^3
  • Lateral surface area = 4a2
  • Surface Area: S = 6s^2
  • Diagonal (d) = s√3

Cuboid

cuboid

  • Volume of cuboid: length x breadth x width
  • Total surface area = 2 ( lb + bh + hl)

Right  Circular  Cylinder

cylinder

  • Volume of Cylinder = π r^2 h
  • Lateral Surface Area (LSA or CSA) = 2π r h
  • Total Surface Area = TSA = 2 π r (r + h)

Right Circular Cone

cone

  • l^2 = r^2 + h^2
  • Volume of cone = 1/3 π r^2 h
  • Curved surface area: CSA=  π r l
  • Total surface area = TSA = πr(r + l )

Frustum of a Cone

frustram cone

  • r = top radius, R = base radius,
  • h = height, s = slant height
  • Volume: V = π/ 3 (r^2 + rR + R^2)h
  • Surface Area: S = πs(R + r) + πr^2 + πR^2

Sphere

sphere

  • r = radius
  • Volume: V = 4/3 πr^3
  • Surface Area: S = 4π^2

Hemisphere

hemisphere

  • Volume-Hemisphere = 2/3 π r^3
  • Curved surface area(CSA) = 2 π r^2
  • Total surface area = TSA = 3 π r^2

Prism

  • Volume = Base area x height

prism 1

  • Lateral Surface area = perimeter of the base x height

prism 2

Pyramid

pyramid

  • Volume of a right pyramid = (1/3) × area of the base × height.
  • Area of the lateral faces of a right pyramid = (1/2) × perimeter of the base x slant height.
  • Area of whole surface of a right pyramid = area of the lateral faces + area of the base.

 

 

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