CBSE Class 8 Mathematics Visualising Solid Shapes MCQs Set 23

Mathematics Objective Questions and Answers: Chapter 10 Visualising Solid Shapes

Explore reliable objective questions for Chapter 10 Visualising Solid Shapes tailored for Class 8 learners. Utilizing these Mathematics multiple-choice formats ensures thorough preparation and strengthens problem-solving speed for upcoming school assessments.

Download Chapter 10 Visualising Solid Shapes MCQs with Answers

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Multiple Choice Questions

Question 1: The number of faces of a pentagonal prism is:
(a) 8
(b) 6
(c) 7
(d) 10
Show Answer & Explanation

Answer: (c) 7

Explanation:
1. A prism has two congruent pentagonal bases and 5 rectangular side faces.
2. Faces = 5 + 2 = 7.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 2: The number of vertices of a pentagonal prism is:
(a) 7
(b) 12
(c) 10
(d) 5
Show Answer & Explanation

Answer: (c) 10

Explanation:
1. Each of the two bases has 5 vertices.
2. Vertices = 2 x 5 = 10.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 3: The number of edges of a pentagonal prism is:
(a) 17
(b) 16
(c) 10
(d) 15
Show Answer & Explanation

Answer: (d) 15

Explanation:
1. Each base has 5 edges and there are 5 lateral edges.
2. Edges = 3 x 5 = 15.
3. Check: f + v = 7 + 10 = 17 = e + 2.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 4: The number of vertices of a hexagonal prism is:
(a) 14
(b) 8
(c) 6
(d) 12
Show Answer & Explanation

Answer: (d) 12

Explanation:
1. Each of the two bases has 6 vertices.
2. Vertices = 2 x 6 = 12.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 5: The number of edges of a hexagonal prism is:
(a) 20
(b) 18
(c) 19
(d) 12
Show Answer & Explanation

Answer: (b) 18

Explanation:
1. Each base has 6 edges and there are 6 lateral edges.
2. Edges = 3 x 6 = 18.
3. Check: f + v = 8 + 12 = 20 = e + 2.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 6: The number of faces of a octagonal prism is:
(a) 16
(b) 11
(c) 9
(d) 10
Show Answer & Explanation

Answer: (d) 10

Explanation:
1. A prism has two congruent octagonal bases and 8 rectangular side faces.
2. Faces = 8 + 2 = 10.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 7: The number of vertices of a octagonal prism is:
(a) 10
(b) 16
(c) 8
(d) 18
Show Answer & Explanation

Answer: (b) 16

Explanation:
1. Each of the two bases has 8 vertices.
2. Vertices = 2 x 8 = 16.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 8: The number of edges of a octagonal prism is:
(a) 25
(b) 24
(c) 16
(d) 26
Show Answer & Explanation

Answer: (b) 24

Explanation:
1. Each base has 8 edges and there are 8 lateral edges.
2. Edges = 3 x 8 = 24.
3. Check: f + v = 10 + 16 = 26 = e + 2.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 9: The number of faces of a triangular prism is:
(a) 7
(b) 5
(c) 4
(d) 6
Show Answer & Explanation

Answer: (b) 5

Explanation:
1. A prism has two congruent triangular bases and 3 rectangular side faces.
2. Faces = 3 + 2 = 5.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 10: The number of edges of a triangular prism is:
(a) 9
(b) 6
(c) 11
(d) 10
Show Answer & Explanation

Answer: (a) 9

Explanation:
1. Each base has 3 edges and there are 3 lateral edges.
2. Edges = 3 x 3 = 9.
3. Check: f + v = 5 + 6 = 11 = e + 2.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 11: The number of faces of a heptagonal prism is:
(a) 10
(b) 14
(c) 8
(d) 9
Show Answer & Explanation

Answer: (d) 9

Explanation:
1. A prism has two congruent heptagonal bases and 7 rectangular side faces.
2. Faces = 7 + 2 = 9.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 12: The number of vertices of a heptagonal prism is:
(a) 9
(b) 16
(c) 14
(d) 7
Show Answer & Explanation

Answer: (c) 14

Explanation:
1. Each of the two bases has 7 vertices.
2. Vertices = 2 x 7 = 14.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 13: The number of edges of a heptagonal prism is:
(a) 22
(b) 21
(c) 14
(d) 23
Show Answer & Explanation

Answer: (b) 21

Explanation:
1. Each base has 7 edges and there are 7 lateral edges.
2. Edges = 3 x 7 = 21.
3. Check: f + v = 9 + 14 = 23 = e + 2.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 14: The number of faces of a decagonal prism is:
(a) 20
(b) 11
(c) 13
(d) 12
Show Answer & Explanation

Answer: (d) 12

Explanation:
1. A prism has two congruent decagonal bases and 10 rectangular side faces.
2. Faces = 10 + 2 = 12.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 15: The number of vertices of a decagonal prism is:
(a) 20
(b) 12
(c) 22
(d) 10
Show Answer & Explanation

Answer: (a) 20

Explanation:
1. Each of the two bases has 10 vertices.
2. Vertices = 2 x 10 = 20.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 16: The number of faces of a pentagonal pyramid is:
(a) 7
(b) 5
(c) 10
(d) 6
Show Answer & Explanation

Answer: (d) 6

Explanation:
1. A pyramid has one pentagonal base and 5 triangular faces.
2. Faces = 5 + 1 = 6.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 17: The number of edges of a pentagonal pyramid is:
(a) 5
(b) 9
(c) 15
(d) 10
Show Answer & Explanation

Answer: (d) 10

Explanation:
1. There are 5 edges in the base and 5 edges meeting at the apex.
2. Edges = 10.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 18: The number of vertices of a pentagonal pyramid is:
(a) 10
(b) 6
(c) 7
(d) 5
Show Answer & Explanation

Answer: (b) 6

Explanation:
1. 5 vertices of the base plus 1 apex = 6.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 19: The number of faces of a hexagonal pyramid is:
(a) 8
(b) 12
(c) 7
(d) 6
Show Answer & Explanation

Answer: (c) 7

Explanation:
1. A pyramid has one hexagonal base and 6 triangular faces.
2. Faces = 6 + 1 = 7.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 20: The number of edges of a hexagonal pyramid is:
(a) 6
(b) 18
(c) 12
(d) 11
Show Answer & Explanation

Answer: (c) 12

Explanation:
1. There are 6 edges in the base and 6 edges meeting at the apex.
2. Edges = 12.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 21: The number of vertices of a hexagonal pyramid is:
(a) 8
(b) 12
(c) 6
(d) 7
Show Answer & Explanation

Answer: (d) 7

Explanation:
1. 6 vertices of the base plus 1 apex = 7.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 22: The number of edges of a square pyramid is:
(a) 12
(b) 4
(c) 7
(d) 8
Show Answer & Explanation

Answer: (d) 8

Explanation:
1. There are 4 edges in the base and 4 edges meeting at the apex.
2. Edges = 8.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 23: The number of vertices of a square pyramid is:
(a) 8
(b) 4
(c) 6
(d) 5
Show Answer & Explanation

Answer: (d) 5

Explanation:
1. 4 vertices of the base plus 1 apex = 5.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 24: The number of faces of a octagonal pyramid is:
(a) 10
(b) 8
(c) 16
(d) 9
Show Answer & Explanation

Answer: (d) 9

Explanation:
1. A pyramid has one octagonal base and 8 triangular faces.
2. Faces = 8 + 1 = 9.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 25: The number of edges of a octagonal pyramid is:
(a) 24
(b) 8
(c) 16
(d) 15
Show Answer & Explanation

Answer: (c) 16

Explanation:
1. There are 8 edges in the base and 8 edges meeting at the apex.
2. Edges = 16.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 26: The number of vertices of a octagonal pyramid is:
(a) 16
(b) 10
(c) 9
(d) 8
Show Answer & Explanation

Answer: (c) 9

Explanation:
1. 8 vertices of the base plus 1 apex = 9.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 27: A polyhedron has 6 faces and 8 vertices. By Euler's formula the number of edges is:
(a) 14
(b) 11
(c) 12
(d) 13
Show Answer & Explanation

Answer: (c) 12

Explanation:
1. Euler's formula: f + v = e + 2.
2. Solving gives 12 edges.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 28: A polyhedron has 12 faces and 20 vertices. By Euler's formula the number of edges is:
(a) 29
(b) 30
(c) 31
(d) 32
Show Answer & Explanation

Answer: (b) 30

Explanation:
1. Euler's formula: f + v = e + 2.
2. Solving gives 30 edges.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 29: A polyhedron has 20 faces and 30 edges. By Euler's formula the number of vertices is:
(a) 12
(b) 14
(c) 13
(d) 11
Show Answer & Explanation

Answer: (a) 12

Explanation:
1. Euler's formula: f + v = e + 2.
2. Solving gives 12 vertices.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

Question 30: A polyhedron has 20 vertices and 30 edges. By Euler's formula the number of faces is:
(a) 13
(b) 14
(c) 11
(d) 12
Show Answer & Explanation

Answer: (d) 12

Explanation:
1. Euler's formula: f + v = e + 2.
2. Solving gives 12 faces.

Teacher's Note:
1. Use Euler's formula f + v = e + 2 to check counts of faces, vertices and edges.
2. A prism on an n-sided base has n + 2 faces, 2n vertices and 3n edges; a pyramid has n + 1 faces, n + 1 vertices and 2n edges.

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FAQs

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