Tabulate the number of faces, edges and vertices for the following polyhedrons: (Here, 'V' stands for number of vertices, 'F' stands for number of faces and 'E' stands for number of edges).

Solid	F	V	E	F+V	E+2
Cuboid
Triangular pyramid
Triangular prism
Pyramid with square base
Prism with square base

What do you infer from the last two columns? In each case, do you find F + V = E + 2, i.e. F + V - E = 2?

5

(a)

What happens to F, V and E, if some parts are sliced off from a solid? (To start with, you may take a plasticine cube, cut a corner off and investigate.)

5

(a)

Using Euler’s formula find the unknown

Faces	?	5	20
Vertices	6	?	12
Edges	12	9	?

5

(a)

The following is the map of a town. Based on it answer the questions.

(a) Find the number of hospitals in the town,
(b) Find the ratio of the number of general stores to the ground,
(c) According to the map, find the number of schools in the town,
(d) What is the value depicted by the map of a particular location?

5

(a)

Use isometric dot paper, to sketch a rectangular prism with length 4 units, height 2 units and width 3 units

5

(a)

A polyhedron has 20 faces and 12 vertices. Find the edges of the polyhedron.

5

(a)

A solid has 40 faces and sixty edges. Find the number of vertices.

5

(a)

The actual width of a store room is 320 cm. If the scale chosen to make its drawing is 1:4, then find the width of the room in the drawing.

5

(a)

The scale on a map is 1 m: 9 m. Find the distance on the map for an actual distance of 63 m.

5

(a)

A solid has 20 faces and double edges to its faces. Find the number of vertices.

5

(a)