CTET · Study & Practice

Solids Around Us (3-D Shapes)

AreaMathematics & Pedagogy DifficultyEasy CTET weightage2-3 questions in the Mathematics section of CTET Paper 1 (geometry of solids is a steady favourite)

Walk into any primary classroom and the maths is sitting on the desks: the chalk box is a cuboid, the duster is roughly a cuboid, the bell on the table is a cylinder, the ball in the corner is a sphere. That is exactly the spirit of this chapter. CTET Paper 1 does not ask you to compute the volume of a cone here. It asks you to recognise the five common solids, recall how many faces, edges and corners each one has, and match each shape to the everyday objects a young child would actually point at. The questions are short and factual, but they trip people up in two ways: confusing a flat 2-D circle with a solid 3-D sphere, and miscounting the faces of a cylinder or cone. Get the five shapes cold, keep the real-life examples handy, and this becomes one of the most reliable mark-scoring topics in the paper.

Topics

1 Identification of Solids 4 worked · 4 practice · 8-Q MCQ test Start → 2 Properties of Solids 4 worked · 4 practice · 8-Q MCQ test Start → 3 Real-Life Examples 4 worked · 4 practice · 8-Q MCQ test Start → 4 Sorting and Classification 4 worked · 4 practice · 8-Q MCQ test Start →

⚡ Smart tips & memory hooks

Memory hooks and exam-smart tips to lock this chapter in and answer CTET MCQs quickly and accurately.

  • Box family = same numbers: cube and cuboid both have 6 faces, 12 edges, 8 vertices. Cube has square faces; cuboid has rectangular faces.
  • Count a cylinder as 3 faces (2 flat circles + 1 curved), 2 edges, 0 vertices - the most commonly miscounted solid.
  • A cone has exactly 1 vertex (the apex), 1 edge and 2 faces (1 flat + 1 curved). Do not write 0 vertices.
  • A sphere is the "all zeros" solid: 1 curved surface, 0 edges, 0 vertices.
  • Curved surface = can roll. So sphere, cylinder and cone roll; cube and cuboid do not.
  • A coin or a CD looks like a circle but has thickness, so it is a cylinder (2-D circle vs 3-D solid is the classic CTET trap).

⚠️ Common mistakes & traps

CTET loves to test these exact confusions. Internalise each trap before exam day.

  • Calling a coin, plate or CD a "circle" - a circle is a flat 2-D shape; these objects have thickness and are short cylinders.
  • Saying a cylinder has 2 faces - it has 3 (two flat circles plus one curved surface).
  • Writing that a cone has 0 vertices - it has 1 vertex, the apex at the tip.
  • Giving a sphere edges or vertices - it has none; only a single curved surface.
  • Mixing up a cube and a cuboid - both have 6/12/8, but the cube has equal square faces while the cuboid has rectangular faces.
  • Confusing faces with edges or vertices - a face is a surface, an edge is a meeting line, a vertex is a corner point.

📈 CTET exam insight & PYQ analysis

In CTET Paper 1 Mathematics, solids appear as short, direct factual questions, usually 2-3 across the section. The most common patterns are: counting the faces, edges or vertices of a named solid (the cylinder, cone and sphere are favourite traps); matching an everyday object to its solid (dice-cube, brick-cuboid, ball-sphere, can-cylinder, ice-cream cone-cone); and the 2-D-versus-3-D distinction, where a coin or a sheet of paper is offered to test whether candidates know a flat shape from a solid. Pedagogy-flavoured items ask which classroom activity (a geometry hunt or hands-on sorting) best builds spatial and classification skills, and which solids can roll or stack - linking the geometry to how young children actually learn it.

🎴 Flashcards — instant recall

Tap a card to reveal the answer. Drill these until they are automatic.

Faces, edges, vertices of a cube?Tap to reveal
6 faces, 12 edges, 8 vertices (all faces are equal squares)
Faces, edges, vertices of a cuboid?Tap to reveal
6 faces, 12 edges, 8 vertices (faces are rectangles)
Faces, edges, vertices of a cylinder?Tap to reveal
3 faces (2 flat + 1 curved), 2 edges, 0 vertices
Faces, edges, vertices of a cone?Tap to reveal
2 faces (1 flat + 1 curved), 1 edge, 1 vertex (apex)
Faces, edges, vertices of a sphere?Tap to reveal
1 curved surface, 0 edges, 0 vertices
Which solids can roll?Tap to reveal
Sphere, cylinder and cone - all have a curved surface
Which solids can be stacked stably?Tap to reveal
Cube, cuboid and cylinder - they have flat faces to rest on
A dice is which solid?Tap to reveal
A cube (6 equal square faces)
A brick is which solid?Tap to reveal
A cuboid (6 rectangular faces)
A cold-drink can is which solid?Tap to reveal
A cylinder
An ice-cream cone is which solid?Tap to reveal
A cone
Is a coin a circle or a cylinder?Tap to reveal
A cylinder - it has thickness; a circle is a flat 2-D shape

📌 Quick revision

Solids are 3-D shapes that occupy space, with length, breadth and height, unlike flat 2-D shapes. The five everyday solids are the cube (6 square faces, 12 edges, 8 vertices), the cuboid (6 rectangular faces, 12 edges, 8 vertices), the cylinder (3 faces - 2 flat circles plus 1 curved - 2 edges, 0 vertices), the cone (2 faces, 1 edge, 1 vertex at the apex) and the sphere (1 curved surface, 0 edges, 0 vertices). Describe them using faces (surfaces), edges (meeting lines) and vertices (corners). Match each to real objects - dice/cube, brick/cuboid, can/cylinder, ice-cream cone/cone, ball/sphere - and watch the classic trap that a coin is a short cylinder, not a circle. Children learn this best by hunting for and sorting real objects (which roll, which stack, which have a flat face or a vertex), turning identification into early logical classification.

Chapter test

📝 Solids Around Us (3-D Shapes) — Chapter Test
25 fresh questions · timed · full solutions
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🏆 Vidaara CTET success checklist

You have truly mastered Solids Around Us (3-D Shapes) when you can tick every box below.

  • Recall every formula in this chapter without looking them up
  • Solve each topic’s practice set with at least 80% accuracy
  • Use the chapter shortcuts to cut your solving time in half
  • Spot and avoid every common trap listed above
  • Score 80%+ on the timed chapter test

📋 Chapter mastery scorecard

Track where you stand. Aim for the target before moving to the next chapter.

Skill checkpointTarget
Concept theory & formulas understood100%
Topic practice sets attempted (4 topics)4/4
Best topic-test score— → 80%+
Chapter test score— → 80%+
Flashcards drilled to instant recall12 cards