Name: Euler's Formula
Uploaded: 2019-07-19
Duration: 2 min 6 s
Description: Euler’s formula defines the relationship among the number of vertices, the number of faces, and the number of edges of a polyhedron. Watch the video and lear...

Question

Using Euler's formula, find the unknown in the table given below.

Faces	$8$	$5$	$x_{1}$
Vertices	$x_{2}$	$6$	$12$
Edges	$12$	$x_{3}$	$30$

Accepted Answer

According to Euler’s formula, in any polyhedron, $F + V - E = 2$ , where ‘ $F$ ’ stands for the number of faces, ‘ $V$ ’ stands for the number of vertices and ‘ $E$ ’ stands for the number of edges.

(i) Number of faces, $F = 8$

Number of edges, $E = 12$

Number of vertices, $V = x_{2}$

According to Euler’s formula in any polyhedron,

$\Rightarrow 8 + x_{2} - 12 = 2$

$\Rightarrow x_{2} - 4 = 2$

$\Rightarrow x_{2} = 2 + 4 = 6$

(ii) Number of faces, $F = 5$

Number of vertices, $V = 6$

Number of edges, $E = x_{3}$

According to Euler’s formula in any polyhedron,

$5 + 6 - x_{3} = 2$

$12$

$\Rightarrow x_{3} = 11 - 2 = 9$

(iii) Number of faces, $F = x_{1}$

Number of edges, $E = 30$

Number of vertices, $V = 12$

According to Euler’s formula in any polyhedron,

$x_{1} + 12 - 30 = 2$

$\Rightarrow x_{1} - 18 = 2$

$\Rightarrow x_{1} = 2 + 18 = 20$

Faces $8$ $5$ $20$

Vertices $6$ $6$ $12$

Edges $12$ $9$ $30$

Using Euler's formula, find the unknown in the table given below.

Faces $8$ $5$ $x_{1}$

Vertices $x_{2}$ $6$ $12$

Edges $12$ $x_{3}$ $30$

Important Questions on Visualising Solid Shapes

Learn and Prepare for any exam you want !

Using Euler's formula, find the unknown in the table given below. Faces 8 5 x1 Vertices x2 6 12 Edges 12 x3 30

Important Questions on Visualising Solid Shapes

Learn and Prepare for any exam you want !

Using Euler's formula, find the unknown in the table given below.

Faces $8$ $5$ $x_{1}$

Vertices $x_{2}$ $6$ $12$

Edges $12$ $x_{3}$ $30$