Mensuration (3D) Formulas Tips And Tricks

Mensuration (3D) Formulas Tips And Tricks

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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.

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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