## ML Aggarwal Class 8 Visualising Solid Shapes Check Your Progress

Question 1.

Write the number of faces, vertices and edges of a

(i) hexagonal pyramid

(ii) octagonal pyramid

(iii) decagonal pyramid

(iv) nonagonal pyramid

(v) heptagonal prism

(vi) decagonal prism.

Solution:

Faces | Vertices | Edges | |

(i) hexagonal pyramid | 7 | 7 | 12 |

(ii) octagonal pyramid | 9 | 9 | 16 |

(iii) decagonal pyramid | 11 | 11 | 20 |

(iv) nonagonal pyramid | 10 | 10 | 18 |

(v) heptagonal prism | 9 | 14 | 21 |

(vi) decagonal prism | 12 | 20 | 30 |

Question 2.

Give three examples of 3-dimensional shapes around you which are the combinations of 2 or more 3-dimensional shapes.

Solution:

3-dimensional shapes which are the combination of

2 or more 3-dimensional shapes.

(i) A funnel: Combination of cone and cylinder.

(ii) A toy: Combination of a cone and hemisphere.

(iii) An ice-cream cone: Combination of a cone and hemisphere.

(iv) A circus tent: Combination of a cylinder and a cone.

Question 3.

Give two examples of solids which are not polyhedrons.

Solution:

Sides which are not polyhedron:

(i) Cylinder

(ii) Sphere

(iii) Cone

Question 4.

Why a pentagonal pyramid having all its edges congruent cannot be a regular polyhedron?

Solution:

A pentagonal pyramid having all its edges congruent cannot be a regular

polyhedron because all the vertices of it are not formed by the same number of faces.

Question 5.

In a polyhedron, if F = 8 and V = 12 then find the number of edges.

Solution:

In a polyhedron,

F = 8, V = 12, then edges

F + V = E + 2

⇒ E = F + V- 2

⇒ Edges = 8 + 12 – 2 = 18

Question 6.

Verify Euler’s formula for the following figures:

Solution:

Question 7.

For each of the given solid, the three views are given. Identify for each solid the corresponding top, front and side views:

Solution:

(a) A television

(i) Front view

(ii) Side view

(iii) Top view

(b) An aeroplane

(i) Front view

(ii) Side view

(iii) Top view

(c) A prism

(i) Top view

(ii) Front view

(iii) Side view

(d) A car

(i) Front view

(ii) Side view

(iii) Top view