10

Q1. What is the number of edges in a pyramid with pentagon as base?

• 12
• 10
• 6
• 8

Solution

For a pentagonal pyramid, F = 6, V = 6Applying Euler's formula: F + V - E = 2                E =  F + V - 2                E = 6 + 6 - 2                E = 10

Q2. What is the number of vertices in prism with triangular base?

• 6
• 5
• 8
• 10

Solution

For a triangular prism, F = 5, E = 9Applying Euler's formula: F + V - E = 2                V = 2 + E - F                V = 2 + 9 - 5                V = 6

Q3. What is the number of faces in a polyhedron with 10 edges and 6 vertices?

• 4
• 6
• 5
• 8

Solution

For the given polyhedron, V = 6, E = 10Applying Euler's formula: F + V - E = 2                F = 2 + E - V                F = 2 + 10 - 6                F = 6

Q4. What is the number of faces in a hexagonal pyramid?

• 6
• 7
• 8
• 9

Solution

For a hexagonal pyramid, V=7, E = 12Applying Euler's formula: F + V - E = 2                F = 2 + E - V                F = 2 + 12 - 7                F = 7

Q5. Which of the following two statements must be true for a regular polyhedron? Statement I : Its faces are congruent.Statement II : Its vertices are formed by same number of faces.

• Only I
• Only II
• Either I or II
• Both I & II

Solution

Follows from definition

Q6. If a prism is a regular polyhedron, its base must be?

• Triangular
• Hexagonal
• Pentagon
• Square

Solution

Square because regular polyhedron has its faces congruent and regular polygons. Also its vertices are formed by same number of faces.

Q7. Which of the following is a regular polyhedron?

• Square Pyramid
• Square Prism
• Cube
• Cuboid

Solution

Cube because its faces are congruent and regular polygons.

Q8. In a map, ______ are used to represent different objects.

• Lines
• Symbols
• Circles
• Squares

Solution

Symbols

Q9. Number of faces in a triangular prism is:

• 4
• 6
• 7
• 5

Solution

A triangular prism has 5 faces.

Q10. Number of faces in a sphere is:

• 1
• 2
• 0
• 4