CBSE Class 8 Mathematics Visualising Solid Shapes MCQs Set 32

Practice MCQs for Class 8 Mathematics 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.

Access Chapter 10 Visualising Solid Shapes Questions and Solutions

View or download the dedicated Chapter 10 Visualising Solid Shapes MCQ resource below. Practicing these 50 objective questions regularly builds familiarity with standard exam patterns and helps secure higher marks in final Mathematics evaluations.

Multiple Choice Questions

Question 1: A polyhedron has 7 faces and 10 vertices. By Euler's formula the number of edges is:
(a) 14
(b) 16
(c) 17
(d) 15
Show Answer & Explanation

Answer: (d) 15

Explanation:
1. Euler's formula: f + v = e + 2.
2. Solving gives 15 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 2: A polyhedron has 9 faces and 14 vertices. By Euler's formula the number of edges is:
(a) 22
(b) 21
(c) 20
(d) 23
Show Answer & Explanation

Answer: (b) 21

Explanation:
1. Euler's formula: f + v = e + 2.
2. Solving gives 21 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 3: A polyhedron has 6 faces and 6 vertices. By Euler's formula the number of edges is:
(a) 11
(b) 12
(c) 10
(d) 9
Show Answer & Explanation

Answer: (c) 10

Explanation:
1. Euler's formula: f + v = e + 2.
2. Solving gives 10 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 4: Euler's formula for a polyhedron with f faces, v vertices and e edges is:
(a) v + e = f + 2
(b) f + v + e = 2
(c) f + v = e + 2
(d) f + e = v + 2
Show Answer & Explanation

Answer: (c) f + v = e + 2

Explanation:
1. Euler found that for every polyhedron the sum of faces and vertices exceeds the number of edges by 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 5: For a cuboid, f + v - e equals:
(a) 0
(b) 2
(c) 4
(d) 1
Show Answer & Explanation

Answer: (b) 2

Explanation:
1. f = 6, v = 8, e = 12.
2. 6 + 8 - 12 = 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: Which of the following is NOT a polyhedron?
(a) Triangular prism
(b) Cone
(c) Pentagonal pyramid
(d) Cuboid
Show Answer & Explanation

Answer: (b) Cone

Explanation:
1. A polyhedron is bounded only by polygonal faces.
2. A cone has a curved surface, so it is not a polyhedron.

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: A solid shape bounded by polygons, called faces, which meet at edges and vertices is called a:
(a) cylinder
(b) sphere
(c) cone
(d) polyhedron
Show Answer & Explanation

Answer: (d) polyhedron

Explanation:
1. This is the definition of a polyhedron.

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: How many regular polyhedra (Platonic solids) are there?
(a) 4
(b) 5
(c) 3
(d) 6
Show Answer & Explanation

Answer: (b) 5

Explanation:
1. The five Platonic solids are the tetrahedron, cube, octahedron, dodecahedron and icosahedron.

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 Platonic solid with 8 triangular faces is the:
(a) tetrahedron
(b) icosahedron
(c) octahedron
(d) dodecahedron
Show Answer & Explanation

Answer: (c) octahedron

Explanation:
1. Octa means eight; the octahedron has 8 equilateral triangles, 12 edges and 6 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 10: A dodecahedron has how many faces and of what shape?
(a) 12 triangular faces
(b) 12 pentagonal faces
(c) 10 pentagonal faces
(d) 20 pentagonal faces
Show Answer & Explanation

Answer: (b) 12 pentagonal faces

Explanation:
1. Dodeca means twelve.
2. Its faces are 12 regular pentagons; it has 30 edges and 20 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 11: A regular polyhedron with 20 triangular faces, 30 edges and 12 vertices is called an:
(a) octahedron
(b) icosahedron
(c) tetrahedron
(d) dodecahedron
Show Answer & Explanation

Answer: (b) icosahedron

Explanation:
1. The icosahedron has 20 equilateral triangular faces.
2. Check: 20 + 12 = 32 = 30 + 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 12: The tetrahedron has:
(a) 6 faces, 4 edges and 4 vertices
(b) 4 faces, 6 edges and 4 vertices
(c) 4 faces, 4 edges and 6 vertices
(d) 4 faces, 6 edges and 6 vertices
Show Answer & Explanation

Answer: (b) 4 faces, 6 edges and 4 vertices

Explanation:
1. It is a pyramid on a triangular base.
2. 4 + 4 = 6 + 2, confirming Euler's formula.

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: Another name for a cube is a:
(a) octahedron
(b) hexahedron
(c) tetrahedron
(d) prism with 5 faces
Show Answer & Explanation

Answer: (b) hexahedron

Explanation:
1. A cube has 6 square faces, and hexa means six.

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: A solid whose two faces are congruent polygons in parallel planes and whose other faces are parallelograms is a:
(a) sphere
(b) prism
(c) pyramid
(d) cone
Show Answer & Explanation

Answer: (b) prism

Explanation:
1. This is the definition of a prism.

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 faces, edges and vertices of a cylinder (counting only flat faces and the circular edges) are respectively:
(a) 3 faces, 2 edges and 0 vertices
(b) 2 faces, 2 edges and 0 vertices
(c) 3 faces, 3 edges and 1 vertex
(d) 2 faces, 3 edges and 2 vertices
Show Answer & Explanation

Answer: (a) 3 faces, 2 edges and 0 vertices

Explanation:
1. A cylinder has two flat circular faces and one curved face, so 3 faces.
2. It has two circular edges and no 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 16: How many edges does a cone have (counting the circular edge of the base)?
(a) 2
(b) 3
(c) 1
(d) 0
Show Answer & Explanation

Answer: (c) 1

Explanation:
1. A cone has one circular edge, where the curved surface meets the base.
2. It has one vertex (the apex) and two 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.

Question 17: A pentagonal prism has 15 edges. How many faces does it have by Euler's formula, given that it has 10 vertices?
(a) 8
(b) 6
(c) 7
(d) 5
Show Answer & Explanation

Answer: (c) 7

Explanation:
1. f + 10 = 15 + 2, so f = 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 18: Dice are cubes in which the numbers on opposite faces add up to 7. The number on the face opposite to 4 is:
(a) 3
(b) 5
(c) 4
(d) 2
Show Answer & Explanation

Answer: (a) 3

Explanation:
1. Opposite faces sum to 7: 7 - 4 = 3.

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: On a dice whose opposite faces add up to 7, the three faces meeting at a corner show 1, 2 and 3. The numbers on the opposite faces are:
(a) 4, 5 and 6 respectively
(b) 3, 2 and 1 respectively
(c) 6, 5 and 4 respectively
(d) 5, 4 and 6 respectively
Show Answer & Explanation

Answer: (c) 6, 5 and 4 respectively

Explanation:
1. Opposite of 1 is 6, of 2 is 5 and of 3 is 4.

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: On a cube whose opposite faces add up to 8, the number opposite to 5 is:
(a) 3
(b) 4
(c) 2
(d) 1
Show Answer & Explanation

Answer: (a) 3

Explanation:
1. 8 - 5 = 3.

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 net of a cylinder consists of:
(a) 2 circles and 1 rectangle
(b) 2 circles and 2 rectangles
(c) 1 circle and a sector
(d) 1 circle and 1 rectangle
Show Answer & Explanation

Answer: (a) 2 circles and 1 rectangle

Explanation:
1. Two circular bases and the curved surface opened out into a rectangle.

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 net of a cone consists of:
(a) 2 circles and a rectangle
(b) 1 circle and a triangle
(c) 1 circle and a sector of a circle
(d) 1 circle and a rectangle
Show Answer & Explanation

Answer: (c) 1 circle and a sector of a circle

Explanation:
1. The base is a circle and the curved surface opens out into a sector.

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 net of a tetrahedron is made of:
(a) 4 triangles
(b) 4 squares
(c) 3 triangles
(d) 6 triangles
Show Answer & Explanation

Answer: (a) 4 triangles

Explanation:
1. A tetrahedron has 4 triangular 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.

Question 24: The net of a hexagonal prism consists of:
(a) 2 hexagons and 6 triangles
(b) 2 hexagons and 6 rectangles
(c) 6 hexagons and 2 rectangles
(d) 1 hexagon and 6 triangles
Show Answer & Explanation

Answer: (b) 2 hexagons and 6 rectangles

Explanation:
1. Two hexagonal bases and 6 rectangular side 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.

Question 25: A net consisting of a square and four triangles folds into a:
(a) tetrahedron
(b) prism with a rectangular base
(c) cube
(d) pyramid with a square base
Show Answer & Explanation

Answer: (d) pyramid with a square base

Explanation:
1. A square base and four triangular faces meeting at a point form a square pyramid.

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: A net consisting of 2 squares and 4 rectangles folds into a:
(a) prism with a hexagonal base
(b) square pyramid
(c) prism with a square base
(d) pyramid with a hexagonal base
Show Answer & Explanation

Answer: (c) prism with a square base

Explanation:
1. Two square faces (top and bottom) and 4 rectangular faces make a square prism.

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: The correct statement about a regular octahedron is that it has:
(a) 6 faces, 12 edges and 8 vertices
(b) 8 faces, 6 edges and 12 vertices
(c) 8 faces, 12 edges and 6 vertices
(d) 8 faces, 12 edges and 8 vertices
Show Answer & Explanation

Answer: (c) 8 faces, 12 edges and 6 vertices

Explanation:
1. Faces are 8 equilateral triangles.
2. 8 + 6 = 12 + 2 confirms Euler's formula.

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: The polyhedron that has the same number of faces as vertices is:
(a) an octahedron
(b) a prism
(c) a pyramid
(d) a cube
Show Answer & Explanation

Answer: (c) a pyramid

Explanation:
1. A pyramid on an n-gon has n + 1 faces and n + 1 vertices.
2. A cube has 6 faces but 8 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 29: A polyhedron is convex if:
(a) it has an even number of faces
(b) any two points on it can be joined by a line segment lying inside or on it
(c) all its faces are triangles
(d) it has no edges
Show Answer & Explanation

Answer: (b) any two points on it can be joined by a line segment lying inside or on it

Explanation:
1. This is the definition of a convex polyhedron.

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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