Std 6 Mathematics · Chapter 1

1. Three-Dimensional Shapes

Solutions to Practice Set 1.1 and Exercise 1, with diagrams. Maharashtra State Board (Balbharati), Grade Six Mathematics.

About the chapter

Objects around us like a box, a ball or a dustbin have length, breadth and height. Such shapes are called three-dimensional shapes. In this chapter, we learn about prisms and pyramids. We count their faces, edges and vertices. We also make shapes from nets.

Key points

A prism has two bottom/top faces. They are of the same shape and size.
A pyramid has only one bottom face. Its other faces are triangles that meet at one point.
A prism or pyramid is named by the shape of its bottom face.
A cube, cuboid, cylinder, cone and sphere are also three-dimensional shapes.
A net is a flat figure. It can be folded to make a three-dimensional shape.

Formulas and terms

Face – a flat or curved surface of a shape.
Edge – the line where two faces meet.
Vertex – the point where edges meet. (Plural: vertices)
Prism with n-sided base – 2n vertices, 3n edges.
Pyramid with n-sided base – n + 1 vertices, 2n edges.

Practice Set 1.1

1Complete the table below.

Triangular prism
6 vertices · 9 edges

Triangular pyramid
4 vertices · 6 edges

Square prism
8 vertices · 12 edges

Square pyramid
5 vertices · 8 edges

Pentagonal prism
10 vertices · 15 edges

Pentagonal pyramid
6 vertices · 10 edges

Pyramid / Prism	Triangular Prism	Triangular Pyramid	Square Prism	Square Pyramid	Pentagonal Prism	Pentagonal Pyramid
Bottom face	Triangular	Triangular	Square	Square	Pentagonal	Pentagonal
No. of vertices	6	4	8	5	10	6
No. of edges	9	6	12	8	15	10
No. of vertical faces	3	3	4	4	5	5
No. of bottom / top faces	2	1	2	1	2	1

How to remember: Let the bottom face have n sides. A prism has 2n vertices and 3n edges. A pyramid has n + 1 vertices and 2n edges.

2Complete the table by writing the names of the shapes that appear in the surrounding area.

Temple dome / spire — Cone

Dustbin — Cylinder

Football — Sphere

Christmas tree — Cone

Book — Cuboid

Object	Name of the shape
Temple dome / spire	Cone
Dustbin	Cylinder
Football	Sphere
Christmas tree	Cone
Book	Cuboid

The first answer (Cone) is given in the textbook as an example.

Exercise 1

1Select the correct option.

(i) What shape will be formed if carrom pieces are placed one on top of the other? — B) Cylinder
Carrom pieces are round and flat. When they are piled up, they form a cylinder.
(ii) By which 2 similar shapes is an hourglass formed? — D) Cone
An hourglass is made of two cones joined at their tips.
(iii) Which of the following shapes is not three-dimensional? — A) Square
A square is a flat figure. It has only length and breadth.

2Draw three-dimensional figures from the numbers given below and write the names.

(i) 5 faces, 5 vertices, 8 edges — Square pyramid

(ii) 1 curved face, no vertex, no edge — Sphere

(iii) 6 faces, 12 edges, 8 vertices — Cuboid

(iv) 1 curved face, 2 circular edges, 2 flat faces — Cylinder

(i) 5 faces, 5 vertices and 8 edges. One face is a square and the other faces are triangles. — Square pyramid
(ii) One curved face, no vertex and no edge. — Sphere
(iii) 6 faces, 12 edges and 8 vertices. — Cuboid (If all faces are equal squares, it is a cube.)
(iv) 1 curved face, 2 flat faces and 2 circular edges. — Cylinder

2. Lines and Angles →