NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes Exercise 10.3

Ques. Determine the minimum number of faces that can enclose a solid. Identify the figure and verify Euler’s formula for it.

Soln: A solid needs a minimum of 4 faces to enclose it completely from all sides. This includes 1 base face and 3 lateral faces.

This figure is a tetrahedron. 

Here, all 4 faces are equilateral triangles. A tetrahedron thus can also be called a triangular pyramid.

Therefore, 

In a triangular pyramid, the no. of faces (F) = 4;

No. of vertices (V) = 4; 

No. of edges (E) = 6. 

Verifying by Euler’s formula, 

F + V – E =2

L.H.S = F + V – E

= 4 + 4 – 6

= 8 – 6

= 2 

= R.H.S

Hence, L.H.S. = R.H.S.

Thus, Euler’s formula is satisfied for a tetrahedron.