Question

(a) Can a polyhedron have 10 faces, 20 edges and 15 vertices? Justify your answer.

(b) A glowing bulb is kept above the following solids. Name the shape of the shadows obtained in each case. Attempt to give a rough sketch of the shadow.


[4 MARKS]

Answer 1

Each part: 2 Marks

(a) By Euler's formula,

F + V - E = 2

Substituting the given values

10 + 15 - 20 = 35 - 20 =15 which is not equal to 2.

A solid needs to satisfy the Euler's formula to be called a polyhedron.

$\Rightarrow$ A polyhedron cannot have 10 faces, 20 edges and 15 vertices.


(b) The shapes of the shadows of these figures will be as follows.

(i) A ball

The shape of the shadow of a ball will be a circle.

(ii) A cylindrical pipe

The shape of the shadow of a circular pipe will be a rectangle.

(iii) A book

The shape of the shadow of a book will be a rectangle.