1.

Verify Euler’s formula for these solids.

Answer»

(i) Here, figure (i) contains 7 faces, 10 vertices and 15 edges.
Using Euler’s formula, we see F + V – E = 2
Putting F = 7, V = 10 and E = 15,
F + V – E = 2
=> 7 + 10 – 5 = 2
=> 17 – 15 = 2
=> 2 = 2
=> L.H.S. = R.H.S.

(ii) Here, figure (ii) contains 9 faces, 9 vertices and 16 edges.
Using Euler’s formula, we see F + V – E = 2

F + V – E = 2
=> 9 + 9 – 16 = 2
=> 18 – 16 = 2
=> 2 = 2
=> L.H.S. = R.H.S.


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