Moderate Level Worksheet

Part A: Subjective Questions - Very Short Answer (1 Mark Each)

In this moderate level, we'll explore nets of solids, Euler's formula, and relationships between faces, vertices, and edges.

Understanding these concepts helps us visualize and analyze complex 3D structures.

1. What is meant by edge in a 3D object?

An edge is a line segment where two faces meetthe line between two faces. (Note: Any similar meaning)

Perfect! Edges are the boundaries where faces join together.

2. What is a net of a solid?

A net is a 2D pattern that folds to form a 3D shapea flat pattern of a solid. (Note: Any similar meaning)

Excellent! Nets help us visualize how 3D shapes are constructed.

3. How many faces does a triangular pyramid (tetrahedron) have?

Answer: faces

Correct! A triangular pyramid has 4 triangular faces.

4. Write one example each of prism and pyramid.

Prism: Triangular prismRectangular prismPentagonal prism (Note: Any prism)

Pyramid: Square pyramidTriangular pyramidPentagonal pyramid (Note: Any pyramid)

Great! Prisms have two identical parallel bases, pyramids have one base.

5. Write the name of a solid that has only one vertex.

Answer:

Perfect! A cone has exactly one vertex at its apex.

Drag each shape to its correct category:

Part A: Section B – Short Answer Questions (2 Marks Each)

1. Write the number of faces, vertices, and edges of:

(a) Cube:

Faces = , Vertices = , Edges =

(b) Cylinder:

Faces = (2 flat + 1 curved), Vertices = , Edges =

Excellent! You know the properties of both shapes.

2. Draw a net of a cube showing all its faces.

Note: Draw on your answer sheet - A net of a cube has squares arranged in a cross or T-shape pattern.

Did you complete your drawing? YesDone

Great! There are 11 different nets possible for a cube.

3. How many edges meet at a vertex of a cube?

Answer: edges

Perfect! At each corner of a cube, exactly 3 edges meet.

4. Write the Euler's formula and verify it for a cuboid.

Euler's Formula: F + V - E =

Verification for Cuboid:

Faces (F) =

Vertices (V) =

Edges (E) =

Checking: F + V - E = 6 + 8 - 12 =

Verified! Euler's formula works for all polyhedra.

5. Write the number of faces, edges, and vertices of a square pyramid.

Faces = (1 square base + 4 triangular faces)

Vertices = (4 base + 1 apex)

Edges = (4 base + 4 lateral)

Excellent! A square pyramid has 5 faces, 5 vertices, and 8 edges.

Part A: Section C – Long Answer Questions (4 Marks Each)

1. Draw the nets of the following solids: (a) Cuboid (b) Cylinder (c) Cone.

Note: Draw these on your answer sheet:

(a) Cuboid: rectangles arranged (center rectangle with 4 around it, 1 on top/bottom)

(b) Cylinder: circles + rectangle

(c) Cone: circle + sector (pie-shaped piece)

Did you complete all three nets? YesDone

Excellent! Nets help us understand how 3D shapes unfold.

2. Verify Euler's formula F + V - E = 2 for: (a) Cube (b) Triangular prism.

(a) Cube:

F = , V = , E =

F + V - E = 6 + 8 - 12 =

(b) Triangular prism:

F = , V = , E =

F + V - E = 5 + 6 - 9 =

Perfect! Euler's formula is verified for both shapes.

3. Explain with examples how a 2D shape helps in forming a 3D object.

When a 2D shape is rotatedextendedmoved through space, it forms a 3D object.

Example 1: A rotated around its diameter forms a .

Example 2: A rotated around one of its sides forms a .

Example 3: A extended/swept forms a .

Great! 2D shapes are the building blocks of 3D objects.

4. Identify the 3D shapes you see in the following objects: Ice cream cone, ball, chalk box, tent, dice, and can. Write their 3D names.

Ice cream cone →

Ball →

Chalk box →

Tent → PyramidCone

Dice →

Can →

Excellent! You can identify 3D shapes in everyday objects.

Part B: Objective Questions - Test Your Knowledge!

Answer these multiple choice questions:

6. Which of the following solids has 0 edges and 0 vertices?

(a) Cylinder (b) Sphere (c) Cone (d) Cuboid

Correct! A sphere is perfectly curved with no edges or vertices.

7. In a cube, the number of edges meeting at each vertex is:

(a) 2 (b) 3 (c) 4 (d) 6

Perfect! At each corner of a cube, exactly 3 edges meet.

8. A prism has ___ faces.

(a) 4 (b) 5 (c) 6 (d) 8

Correct! A triangular prism has 5 faces (this is the most common prism). Note: Different prisms have different numbers of faces.

9. The base of a pyramid is always a:

(a) Plane figure (b) Curved surface (c) Line (d) Circle only

Excellent! A pyramid's base is always a flat polygon (plane figure).

10. The solid used for making dice is:

(a) Cuboid (b) Cube (c) Cylinder (d) Sphere

Perfect! Dice are cubes with all sides equal.

🎉 Outstanding Work! You've Mastered Intermediate 3D Concepts!

Here's what you learned:

• Euler's Formula: F + V - E = 2

  • Works for all polyhedra (solids with flat faces)
  • Example: Cube → 6 + 8 - 12 = 2 ✓

• Nets of Solids: 2D patterns that fold into 3D shapes

  • Cube: 6 squares (11 different arrangements possible)
  • Cuboid: 6 rectangles
  • Cylinder: 2 circles + 1 rectangle
  • Cone: 1 circle + 1 sector

• Classification of Solids:

  • Prisms: Two identical parallel bases (triangular, rectangular, hexagonal)
  • Pyramids: One base with triangular faces meeting at apex
  • Curved Solids: Sphere, cone, cylinder

• Key Properties:

  Shape	Faces	Vertices	Edges
  Triangular Prism	5	6	9
  Square Pyramid	5	5	8
  Triangular Pyramid	4	4	6
  Cylinder	3	0	2

• Special Features:

  • Cone: Only 1 vertex, 1 edge
  • Sphere: 0 vertices, 0 edges, 1 curved face
  • Cube: 3 edges meet at each vertex

• 2D to 3D Transformation:

  • Circle rotated → Sphere/Cylinder
  • Rectangle rotated → Cylinder
  • Polygon extended → Prism

Understanding nets and Euler's formula helps us analyze and construct 3D shapes!