Important Mensuration (3D) Formulas

By Parnab Mallick|Updated : January 14th, 2021

It is very important to have an understanding of different 3D Mensuration formulas to comfortably attempt Maths questions which covers a good portion of the Quant Section of Competitive Exams. Here we are providing you formulas and shortcuts on how to solve mensuration questions.

It is very important to have an understanding of different 3D Mensuration formulas to comfortably attempt Maths questions which covers a good portion of the Quant Section of Competitive Exams. Here we are providing you formulas and shortcuts on how to solve mensuration questions.

Important Mensuration (3D) Formulas

Cube

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

Cuboid

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

Right  Circular  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)

Hollow-Cylinder

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r1 = outer radius

r2 = inner radius

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* Volume of Hollow Cylinder = π(pie) h(r1(Square) - r2(Square))

Right Circular 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 )

Important relation between radius, height and slant height of similar cone.

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Frustum of a 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

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

Hemisphere

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

Quarter-Sphere

Let 'r' is the radius of given diagram. You have to imagine this diagram, this is 1/4th part of Sphere.

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Prism

  • Volume = Base area x height
  • Lateral Surface area = perimeter of the base x height

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.

Important:
1.From a solid cylinder no. of maximum solid cone of same height and radius as cylider are 3.
2.From a solid sphere, no. of maximum solid cone having height and radius equal can be made are 4.
3.From a solid hemisphere, no. of maximum solid cone having height and radius equal can be made are 2.

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