3D Figure Formulas, Concepts, Strategies, Short Tricks, and Tips

Published on 12 August 2025 by

3D Figures is an important topic in Quantitative Aptitude that frequently appears in competitive exams like SSC, Banking, and RRB. It tests your ability to visualize objects in three dimensions and analyze their properties such as faces, edges, vertices, and volumes. In this blog, we will cover the basic concepts of 3D figures, common question types, essential formulas, tricks to solve problems quickly, and more.

What Is 3D Figure in Quantitative Aptitude?

3D Figure questions involve three-dimensional geometric shapes such as cubes, cuboids, spheres, cones, cylinders, pyramids, and prisms. These questions test your understanding of spatial relationships and the ability to calculate properties like volume, surface area, or the number of faces, edges, and vertices.

This topic appears often in exams because it checks your logical reasoning, visualization skills, and mathematical knowledge. You need to interpret diagrams, count hidden edges or vertices, and apply formulas correctly.

Skills required include:

  • Spatial visualization
  • Logical deduction
  • Basic geometry and measurement formulas
  • Ability to decode diagrams and mentally rotate figures
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Why Is 3D Figure Important in Competitive Exams?

3D Figure questions are important as they test both your conceptual clarity and speed. They often carry moderate difficulty but are scoring if you practice well. Due to their straightforward nature and frequent appearance, they are crucial for candidates aiming to clear exams with good marks.

ExamNo. of QuestionsDifficulty
SSC CGL / CHSL1–2Easy
IBPS PO / SBI PO1–2Moderate
RRB NTPC / Group D1Easy
State PSC / Police1–2Moderate

3D Figure Quantitative Aptitude Short Notes

Understanding basic terminology and concepts is key to solving 3D figure questions quickly.

TermDetails
FaceFlat surface of a 3D shape
EdgeLine segment where two faces meet
VertexPoint where edges meet
Cube6 faces, 12 edges, 8 vertices
CuboidRectangular box shape, similar to cube
SpherePerfect round 3D object, no edges or vertices
Cylinder2 circular faces + 1 curved surface
Cone1 circular base + 1 curved surface + 1 vertex
PrismPolyhedron with two parallel faces
PyramidBase polygon + triangular faces meeting at a vertex

Concepts Based on 3D Figures

Concepts based on 3D figures are as follows:

ConceptDetails
Faces of a Cube6 faces
Edges of a Cuboid12 edges
Vertices of a PyramidNumber of base vertices + 1
Volume of Cylinderπr²h (r = radius, h = height)
Surface Area of Sphere4πr²
Volume of Cone(1/3)πr²h

What Are the Types of 3D Figure Questions in Quantitative Aptitude?

3D Figure questions come in various forms. Common types include:

  • Direct: Questions asking about faces, edges, vertices.
  • Puzzle-based: Visual puzzles requiring counting of hidden edges or vertices.
  • Coded (symbol-based): Using symbols or codes to represent different faces or parts.
  • Mixed-concept Quantitative Aptitude: Combining 3D figures with mensuration or algebra.
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3D Figure Formulas for Quantitative Aptitude

Memorizing formulas saves time during exams. Some important ones:

  • Cube Volume = a³ (a = side length)
  • Cube Surface Area = 6a²
  • Cuboid Volume = l × b × h
  • Cuboid Surface Area = 2(lb + bh + hl)
  • Sphere Volume = (4/3)πr³
  • Sphere Surface Area = 4πr²
  • Cylinder Volume = πr²h
  • Cylinder Surface Area = 2πr(h + r)
  • Cone Volume = (1/3)πr²h
  • Cone Surface Area = πr(l + r) (l = slant height)

3D Figure Tricks for SSC CGL and Other Exams

Follow these strategies to solve questions efficiently:

  1. Visualize the figure carefully before counting edges or faces.
  2. Use elimination to discard impossible options.
  3. Remember key counts for standard solids (cube, cuboid, sphere).
  4. Draw rough sketches if diagrams are missing.
  5. Check for hidden edges or vertices in complex figures.
  6. Use formulas smartly—don’t waste time deriving basics during exam.
  7. Practice with memory-based questions from recent exams.

Solved 3D Figure Questions from 2024–25 Exams

1. SSC CGL 2024 Tier 1 (Memory-Based):
Question: How many edges does a cuboid have?
Answer: 12
Explanation: A cuboid has 12 edges formed by the intersections of its 6 faces.

2. IBPS PO Prelims 2024:
Question: Number of vertices in a cube?
Answer: 8
Explanation: Each vertex is the meeting point of 3 edges, total vertices = 8.

3. RRB NTPC 2024:
Question: Find the volume of a cylinder with radius 7 cm and height 10 cm.
Answer: 1540 cm³
Explanation: Volume = πr²h = 3.14 × 7² × 10 = 3.14 × 49 × 10 = 1538.6 ≈ 1540 cm³.

4. SSC CHSL 2025 (Based on recent shift):
Question: How many faces does a cone have?
Answer: 2 (1 circular base + 1 curved surface)
Explanation: Cone has 1 flat base and 1 curved surface, total 2 faces.

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Common Mistakes to Avoid while Solving 3D Figure Questions

Common mistakes to avoid while solving 3D figure questions are as follows:

  1. Not visualizing the figure properly: Always try to sketch or mentally rotate the shape.
  2. Forgetting hidden edges or vertices: Count carefully all edges including invisible ones.
  3. Mixing up formulas: Remember which formula applies to which figure.
  4. Ignoring units in volume or surface area: Always convert units before final answer.
  5. Rushing through without reading carefully: Take time to understand what is asked exactly.

FAQs

Q1. What are symbol-based 3D figure questions?

Questions where shapes or faces are represented by symbols, requiring decoding.

Q2. How to count hidden edges in a 3D figure?

Visualize or sketch the figure to identify all edges, including those not visible directly.

Q3. Which 3D figures are most common in exams?

Cube, cuboid, cylinder, cone, sphere, pyramid.

Q4. Do state PSC exams ask 3D figure questions?

Yes, usually moderate difficulty.

Q5. How to prepare for 3D figures effectively?

Practice questions from past papers and visualize daily objects as 3D figures.