Important Questions for CBSE Class 8 Maths Chapter 10 - Visualising Solid Shapes

Very Short Answer Type Questions (1 Mark)

1. A three dimensional shape is $\_\_\_\_\_\_\_\_\_$object. 

Ans: Solid

2. The most important part of a map is the $\_\_\_\_\_\_\_\_\_$

Ans: Scale

3. What are three views in a solid figure? 

Ans: Front view, side view and top view

4. Name of the solid whose net diagram is given below

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(a) Pyramid

(b) Cone

(c) Cube

(d) Cuboid

Ans: (c) Cube

5. The number of triangular face's of a triangular prism is $\_\_\_\_\_\_\_\_\_$

(a) $1$

(b) $4$

(c) $2$

(d) $3$

Ans: (c) $2$

Short Answer Type Questions (2 – Marks)

6. What are regular polyhedrons?

Ans: A polyhedron is called regular if its faces are made up of regular polygons and the same number of faces meet a vertex.

7. Give two basic differences between a prism and a pyramid?

Ans: (a) Pyramid is a polyhedron in which the base is a polygon whereas a prism is a polyhedron in which the base and top are regular polygons.

(b) The lateral surface are parallelograms in a prism whereas in a pyramid the lateral surfaces are triangles.

8. Give two examples of $2\;{\text{d}}$ and $3\;{\text{d}}$ shapes each.

Ans: $2\;{\text{d}}$ shapes : circle, square.

$3\;{\text{d}}$ shapes = pyramid, cone.

9. How many number of squares are visible in top view and front view of the given figure.

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Ans: Top view $ = 6$ squares

Front view $ = 4$ squares

10. In the given solid identify the top, front and side view.

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(a)

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(b)

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(c)

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Ans:

(a) side view

(b) front view

(c) top view

11. Give Euler's formula and explain each term in it. 

Ans: In a polyhedron, the relationship between the number of faces $({\text{F}})$, vertices $({\text{V}})$, and edges $({\text{E}})$ is given by $F + V - {\text{E}} - 2$.

12. Write the number of faces, number of vertices and number of edges of a prism with rectangular base

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Ans: No. of faces $ = 6$ 

No. of vertices $ = 8$ 

No. of Edges $ = 12$

13. Write the number of faces, number of vertices and number of edges of a pyramid with hexagonal base.

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Ans:

No. of faces $ = 7$ 

No. of vertices $ = 7$

No. of edges $ = 12$

14. In a polyhedron there are $8$ vertices and $12$ edges. Find its number of faces. 

Ans:

${\text{F}} + {\text{V}} - {\text{E}} = 2$

$F + 8 - 12 = 2$

$F = 2 + 12 - 8$

$F = 6$

15. A pyramid with square base has $5$ faces and $8$ edges. By Euler's formula, find the vertices of the pyramid. 

Ans: For a pyramid,

$F = 5,{\text{ }}E = 8,{\text{ }}V = ?$

Using Euler's formula, 

$F + V - E = 2$ 

$5 + V - 8 = 2$

$V = 2 + 8 - 5$

$V = 5$

Short Answer Type Questions (3 – Marks)

16. Draw the front view, side view and top view of the given objects.

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Ans:

(a) Front view

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(b) Top view

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(c) Side view

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17. Can a polyhedron have $10$ faces, $20$ edges and $15$ vertices? Justify your answer.

Ans: $F = 10,{\text{ }}E = 20$ and $V = 15$

Using Euler's formula, 

$F + V - E = 2$

L.H.S:

$F + V - E = 10 + 15 - 20$

$F + V - E = 5$

$\therefore F + V - E \ne 2$

This polyhedron is not possible.

18. Match the following pictures with their shapes.

Ans:

Ans: $1 - b,{\text{ }}2 - c,{\text{ }}3 - a$

19. Define

(a) Face

(b) Edge

(c) Vertex 

Ans: (a) Face$ - {\text{A}}$$3\;{\text{d}}$ solid object is made up of flat surfaces or polygonal regions known as faces.

(b) Edge: In $3\;{\text{d}}$ solid objects, the faces meet at edges.

(c) Vertex: The point where all edges meet is known as a vertex.

20. By using Euler's formula find the unknown?

(a) vertices$ = 12$, Faces$ = 4$, Edges $ - ?$

(b) Faces$ = 5$, Edges$ = 8$, Vertices $ = ?$

(c) Edges$ = 2$, Vertices$ = 3$, Faces $ = ?$ 

Ans: Using Euler 's formula: 

$F + V - E = 2$

(a) $4 + 12 - E = 2$

$E = 16 - 2 = 14$

(b) $5 + V - 8 = 2$

$V = 2 + 8 - 5 = 5$

(c) $F + 3 - 2 = 2$

${\text{F = }}2 + 2 - 3 = 1$

Long Answer Type Questions (4 – Marks)

21. Write an examples for tetrahedron and write the number of triangular faces, vertices and edges. Show it verifies Euler’s formula.

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Ans: Example for tetrahedron$ = $Tent 

Number of triangular faces $ = 4$

Number of Vertices $ = 4$

Number of Edges $ = 6$ 

Euler's formula:

$F + V - E = 2$

$4 + 4 - 6 = 2$

$2 = 2$ 

Hence verified.

22. Write an example for Hexahedron with number of faces, vertices and edges. Show it verifies Euler's formula.

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Ans: Example for Hexahedron$ - $Cube (Die) 

Number of faces $ = 6$

Number of Vertices $ = 8$

Number of Edges $ = 12$

Euler’s formula:

$F + V - E = 2$ 

$6 + 8 - 12 = 2$

$14 - 12 = 2$

$2 = 2$ 

Hence verified.

23. Write a prism with square base and a pyramid with rectangular base. Write the number of edges in each case.

Ans: (a) A prism having a square base has $12$ edges.

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(b) A pyramid with rectangular base has $8$ edges.

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24. Match the net’s with appropriate solids.

Ans: 

\[(a) - \left( {iii} \right)\]

\[(b) - \left( {iv} \right)\]

\[(c) - \left( {ii} \right)\]

\[(d) - \left( i \right)\]

25. What cross sections are obtained when

(i) vertical cut

(ii) horizontal cut

(a) An ice cream cone

(b) A die

(c) A round apple

(d) A circular pipe are done with 

Ans: