CG Board Class 8 Mathematics Chapter 16 Solutions: Figures (Two and Three Dimensional) (आकृतियाँ (द्विविमीय एवं त्रिविमीय)) – 2026-27

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CG SCERT (Chhattisgarh Board) Class 8 Mathematics Solutions | 2026-27 Official Edition

Complete 100% textbook-grounded CG Board Class 8 Mathematics Chapter 16 Solutions: Figures (Two and Three Dimensional) (आकृतियाँ (द्विविमीय एवं त्रिविमीय)) in Bilingual Format (English & Hindi Medium).

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🌐 Select Language / माध्यम चुनें:

V – E + F = 2 or F + V – E = 2

  • V = Vertices
  • E = Edges
  • F = Faces
  1. Cuboid:
  • English: V = 8, E = 12, F = 6 ⇒ V – E + F = 8 – 12 + 6 = 2
  • Hindi: V = 8, E = 12, F = 6 ⇒ V – E + F = 8 – 12 + 6 = 2
  1. Cube:
  • English: V = 8, E = 12, F = 6 ⇒ V – E + F = 8 – 12 + 6 = 2
  • Hindi: V = 8, E = 12, F = 6 ⇒ V – E + F = 8 – 12 + 6 = 2
  1. Tetrahedron / Triangular Pyramid:
  • English: V = 4, E = 6, F = 4 ⇒ V – E + F = 4 – 6 + 4 = 2
  • Hindi: V = 4, E = 6, F = 4 ⇒ V – E + F = 4 – 6 + 4 = 2
  1. Square Pyramid:
  • English: V = 5, E = 8, F = 5 ⇒ V – E + F = 5 – 8 + 5 = 2
  • Hindi: V = 5, E = 8, F = 5 ⇒ V – E + F = 5 – 8 + 5 = 2
  1. Triangular Prism:
  • English: V = 6, E = 9, F = 5 ⇒ V – E + F = 6 – 9 + 5 = 2
  • Hindi: V = 6, E = 9, F = 5 ⇒ V – E + F = 6 – 9 + 5 = 2
Question 1

Construct prepare a cube with the help of…


📝 Question:

Construct (prepare) a cube with the help of a square of 3 cm.**

💡 Solution:

  1. Draw a square ABCD of side 3 cm.
  2. Draw another identical square EFGH of side 3 cm shifted slightly above and to the right.
  3. Join the corresponding vertices: AE, BF, CG, and DH.
  4. The resulting 3D figure with 6 identical square faces of side 3 cm is the required cube.

Question 2

Construct a cylinder of 5 cm length


📝 Question:

Construct a cylinder of 5 cm length.**

💡 Solution:

  1. Draw two identical parallel ellipses (representing the top and bottom circular bases) separated by a vertical distance of 5 cm.
  2. Label the centers O1 and O2 such that O_1O2 = 5 cm.
  3. Join the endpoints of the parallel diameters A_1A2 and B_1B2 with straight vertical line segments.
  4. The resulting figure with two circular bases and one curved surface is the required cylinder of length 5 cm.

Question 3

Construct two triangles at a distance of 5…


📝 Question:

Construct two triangles at a distance of 5 cm in your notebook with the help of a triangular hardboard and construct a triangular prism with its help.**

💡 Solution:

  1. Draw a triangle △ ABC using the triangular board as an outline.
  2. At a parallel distance of 5 cm, draw an identical triangle △ A_1B_1C1.
  3. Join the corresponding vertices: AA1, BB1, and CC1 with straight line segments.
  4. The solid figure formed with 2 triangular faces and 3 rectangular faces is the required triangular prism.

Question 4

Construct a quadrilateral in your notebook


📝 Question:

Construct a quadrilateral in your notebook.**

💡 Solution:

  1. Draw a line segment AB of any suitable length using a ruler.
  2. From point B, draw a line segment BC at an angle.
  3. From point C, draw line segment CD.
  4. Join point D to point A to complete the closed 2D polygon ABCD having 4 sides, 4 angles, and 4 vertices.

Question 5

If there are 4 faces and 4 vertices…


📝 Question:

If there are 4 faces and 4 vertices in a polyhedron, can you tell how many edges will be there in it?**

💡 Solution:

Given

  • Number of Faces (F) = 4
  • Number of Vertices (V) = 4

By Euler’s Formula for Polyhedra

V – E + F = 2

Substituting the given values

4 – E + 4 = 2

8 – E = 2 ⇒ E = 8 – 2 = 6

Therefore, the polyhedron has 6 edges (This figure is a Tetrahedron / Triangular Pyramid).

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