Question

The number of edges of a polyhedron, which has 7 faces and 10 vertices.
15
17
13
14​

Answer 1

Given: The polyhedron has 7 faces and 10 vertices.

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Need to find: How many edge of a polyhedron?

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$\frak{Here}\begin{cases}\sf{\:\;\; F = 7}\\\sf{\;\;\; V = 10}\\\sf{\;\;\; E = \: ?}\end{cases}$

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We know that if we are given with the polyhedron faces and polyhedron vertices, we have the required formula, that is,

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$\sf{:\implies V - E + F = 2}$

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⠀⠀⠀⠀ Here V is the vertices of polyhedron, E is the number edge and F is the Faces of polyhedron, And here in this question we have V = 10, F = 7. So by using the Euler's polyhedron formula we can calculate the number of edges.

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By using the formula and substituting all the given values in the formula, we get:

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$\sf{:\implies 10 - E + 7 = 2}$

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$\sf{:\implies 10 + 7 - E = 2}$

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$\sf{:\implies 17 - E = 2}$

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$\sf{:\implies - E = 2 - 17}$

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$\sf{:\implies - E = -15}$

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$\sf{:\implies \blue{\boxed{\frak{ \pink{E = 15}}}}}$

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$\sf{\therefore \underline{The \: number \: of \: edges \: is \: \textsf{\textbf{15.}}}}$

Answer 2

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$\sf Given \; that \begin{cases} & \sf{Faces \: of \: polyhedron = \: \bf{7}} \\ & \sf{Vertices \: of \: polyhedron = \bf{10}} \end{cases}$

Have to find : The number of edges of the given polyhedron

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${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ As it's already known to us that,

• Faces of polyhedron (Given)
• Vertices of polyhedron (Given)
• Edges of polyhedron (To find)

~ So according to the question and the given data it is already cleared to us that which formula have to implied here..!

${\bf{\underline{\red{F \: + \: V \: - \: E \: = 2}}}}$

• [Where, F denotes Number of faces, V denotes number of vertices and E denotes number of edges]

• [Here, F is 7, V is 10 and E is have to find of the given polyhedron]

~ Now let's put the values according to the formula..!

•↝ F+V-E = 2

•↝ 7+10-E = 2

•↝ 17-E = 2

•↝ -E = 2-17

•↝ -E = -15

•↝ E = 15

• Henceforth, E's value is 15 means number of edges of a polyhedron is 15 here.

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