Important Mensuration (3D) Formulas

By Anand Pandey|Updated : March 1st, 2019

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

Important Mensuration (3D) Formulae

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)

Hollow-Cylinder

byjusexamprep

r1 = outer radius

r2 = inner radius

byjusexamprep

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 )

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

byjusexamprep

byjusexamprep

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

Quarter-Sphere

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

 byjusexamprep

byjusexamprep

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.

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.

More from us:

RRB JE Previous Question Papers PDF

Detailed Syllabus for CBT 1 & CBT 2

To help you with your preparation for RRB JE/CMA/DMS/IT 2019 Exam, BYJU'S Exam Prep has launched RRB JE 2019 CBT 1 Online Test Series in Hindi & English based on the latest pattern. This complete test contains 20 Full-length. While the 1st test of the test series is free, the complete pack costs Rs. 245/- only.

Detailed 100 Days Express Plan for RRB JE & Test Series Link

Download Gradeup, the best gate/ese/ssc je/rrb je app for Preparation

All the best!
Team BYJU'S Exam Prep

Comments

write a comment

Follow us for latest updates