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Chapter 18

Visualising Solid Shapes — Statement I-II Type Questions

Class - 8 ML Aggarwal Understanding ICSE Mathematics

Objective Type Questions - Statement I-II Type Questions

Question 17

Statement I: A sphere is a regular polyhedron.

Statement II: A regular polyhedron has regular polygons as all its faces and same number of faces meet at each vertex.

  1. Statement I is true but Statement II is false.

  2. Statement I is false but Statement II is true.

  3. Both Statement I and Statement II are true.

  4. Both Statement I and Statement II are false.

Answer

A sphere has a curved surface, so it is not made up of polygonal regions. So, a sphere is not a polyhedron and therefore it cannot be a regular polyhedron.

So, Statement I is false.

A polyhedron is said to be a regular polyhedron if all of its faces are regular polygons and the same number of faces meet at each vertex.

So, Statement II is true.

Hence, option 2 is the correct option.

Question 18

Statement I: If a polyhedron has 5 faces and 15 edges, then it has 18 vertices.

Statement II: Euler's formula states that in any polyhedron F + E = V + 2

  1. Statement I is true but Statement II is false.

  2. Statement I is false but Statement II is true.

  3. Both Statement I and Statement II are true.

  4. Both Statement I and Statement II are false.

Answer

Given:

F = 5, E = 15

According to Euler's formula,

F + V = E + 2

⇒ 5 + V = 15 + 2

⇒ 5 + V = 17

⇒ V = 17 - 5

⇒ V = 12

So, the polyhedron has 12 vertices and not 18 vertices.

So, Statement I is false.

Euler's formula states that in any polyhedron F + V = E + 2 and not F + E = V + 2.

So, Statement II is false.

Hence, option 4 is the correct option.

Question 19

Statement I: A heptagonal pyramid has 14 edges.

Statement II: A heptagonal prism has 21 edges.

  1. Statement I is true but Statement II is false.

  2. Statement I is false but Statement II is true.

  3. Both Statement I and Statement II are true.

  4. Both Statement I and Statement II are false.

Answer

In a heptagonal pyramid, the number of sides of the polygonal base is 7.

Number of edges in a pyramid is twice the number of sides of the polygonal base.

Number of edges = 7 × 2 = 14

So, Statement I is true.

In a heptagonal prism, the number of sides of the polygonal base is 7.

Number of edges in a prism is thrice the number of sides of the polygonal base.

Number of edges = 7 × 3 = 21

So, Statement II is true.

Hence, option 3 is the correct option.

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