Questions & Answers

Question

Answers

A. 4

B. 5

C. 6

D. 12

Answer
Verified

Hint: Here we can use Eulerâ€™s formula. The number of faces, the number of vertices and the number of edges of a polyhedron are related by the following formula:

Number of faces + number of vertices = number of edges + 2.

Complete step-by-step answer:

In this problem we have to find out how many edges are there in a cuboid. So, let us first draw a cuboid. We know that a cuboid is a solid figure which has six rectangular faces at right angles to each other.

First we have to know about the vertex, edge and face of a solid figure.

A vertex is a point where two or more line segments meet. Basically a vertex is a corner. Plural of vertex is vertices. So, in this picture the vertices are $A,B,C,D,E,F,G,H$ . So there are 8 vertices in a cuboid.

A face is a single flat surface of a solid object. Like here in this figure the faces are:$ABCD,EFGH,ABFE,DCGH,ADHE,BCGF$

So, there are 6 faces in a cuboid.

An edge is a line segment between two faces. For example here the line segment between the faces $ABCD$ and $DCGH$ is $DC$ .

Now, we know the Eulerâ€™s formula:

Number of faces + number of vertices = number of edges + 2

Let us denote the number of faces by $F$.

Number of vertices by $V$.

Number of edges by $E$.

Therefore, $F+V=E+2...........(1)$

Here, the number of faces are 6. Numbers of vertices are 8. Let us put these values in (1).

$\begin{align}

& 6+8=E+2 \\

& \Rightarrow 14=E+2 \\

& \Rightarrow E=14-2 \\

& \Rightarrow E=12 \\

\end{align}$

Therefore the numbers of edges are 12.

Hence option (e) is correct.

Note: We can count the edges from the picture also. Like the edges are $AB, BC, CD, DA, EF, FG, GH, HE, AE, DH, BF, CG$. So there are 12 edges.

Number of faces + number of vertices = number of edges + 2.

Complete step-by-step answer:

In this problem we have to find out how many edges are there in a cuboid. So, let us first draw a cuboid. We know that a cuboid is a solid figure which has six rectangular faces at right angles to each other.

First we have to know about the vertex, edge and face of a solid figure.

A vertex is a point where two or more line segments meet. Basically a vertex is a corner. Plural of vertex is vertices. So, in this picture the vertices are $A,B,C,D,E,F,G,H$ . So there are 8 vertices in a cuboid.

A face is a single flat surface of a solid object. Like here in this figure the faces are:$ABCD,EFGH,ABFE,DCGH,ADHE,BCGF$

So, there are 6 faces in a cuboid.

An edge is a line segment between two faces. For example here the line segment between the faces $ABCD$ and $DCGH$ is $DC$ .

Now, we know the Eulerâ€™s formula:

Number of faces + number of vertices = number of edges + 2

Let us denote the number of faces by $F$.

Number of vertices by $V$.

Number of edges by $E$.

Therefore, $F+V=E+2...........(1)$

Here, the number of faces are 6. Numbers of vertices are 8. Let us put these values in (1).

$\begin{align}

& 6+8=E+2 \\

& \Rightarrow 14=E+2 \\

& \Rightarrow E=14-2 \\

& \Rightarrow E=12 \\

\end{align}$

Therefore the numbers of edges are 12.

Hence option (e) is correct.

Note: We can count the edges from the picture also. Like the edges are $AB, BC, CD, DA, EF, FG, GH, HE, AE, DH, BF, CG$. So there are 12 edges.

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