### Exercise 10.1

**Question 1.**

For each of the given solid, the two views are given. Match for each solid the corresponding top and front views. The first one is done for you.

**Solution :**

(a) (iii); (iv)

(b); (i); ; (v)

(c); (iv) (ii)

(d) (v); (iii)

(e) (ii); (i)

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**Question 2.**

For each of the given solid, the three views are given. Identify for each solid the corresponding top, front and side views.

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**Solution****:**

(a);(i); Front

(ii) Side

(iii) Top view

(b) (i); Side

(ii) Front

(iii); Top view

(c) (i); Front

(ii); Side

(iii) Top view

(d) (i); Front

(ii); Side

(iii); Top view

**Question 3.**

For each given solid, identify the top view, front view and side view.

**Solution :**

(a); (i) Top view (ii); Front view (iii); Side view

(b) (i) Side view (ii) Front view (iii); Top view

(c); (i); Top view (ii); Side view (iii) Front view

(d); (i) Side view (ii) Front view (iii) Top view

(e) (i); Front view (ii); Top view (iii) Side view

**Question 4.**

Draw the front view, side view and top view of the given objects:

**Solution :**

### NCERT Solutions for Class 8 Maths Exercise 10.2

**Question 1.**

Can a polygon have for its faces:

(i) 3 triangles ;

(ii) 4 triangles

(iii) a square and four triangles

**Solution :**

(i) No, a polyhedron cannot have 3 triangles for its faces.

(ii) Yes, a polyhedron can have four triangles which is known as pyramid on triangular base.

(iii) Yes, a polyhedron has its faces a square and four triangles which makes a pyramid on square base.**Question 2.**

Is it possible to have a polyhedron with any given number of faces? (Hint: Think of a pyramid)

Ans.

It is possible, only if the number of faces are greater than or equal to 4.**Question 3.**

Which are prisms among the following:

**Solution :**

Figure (ii) unsharpened pencil and figure (iv) a box are prisms.

**Question 4.**

(i) How are prisms and cylinders alike?

(ii) How are pyramids and cones alike?

**Solution :**

(i) A prism becomes a cylinder as the number of sides of its base becomes larger and larger.

(ii) A pyramid becomes a cone as the number of sides of its base becomes larger and larger.

**Question 5.**

Is a square prism same as a cube? Explain.

**Solution :**

No, it can be a cuboid also.

**Question 6.**

Verify Euler’s formula for these solids.

**Solution :**

(i) Here, figure (i) contains 7 faces, 10 vertices and 15 edges.

Using Eucler’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 Eucler’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.

Hence verified Eucler’s formula.

**Question 7.**

Using Euler’s formula, find the unknown:

Faces | ? | 5 | 20 |

Vertices | 6 | ? | 12 |

Edges | 12 | 9 | ? |

**Solution :**

In first column, F = ?, V = 6 and

E = 12

Using Eucler’s formula, we see

F + V – E = 2

F + V – E = 2

;F + 6 – 12 = 2

;F – 6 = 2

;F = 2 + 6 = 8

Hence there are 8 faces.

In second column, F = 5, V = ? and E = 9

Using Eucler’s formula, we see

F + V – E = 2

F + V – E = 2

;5 + V – 9 = 2

;V – 4 = 2

;V = 2 + 4 = 6

Hence there are 6 vertices.

In third column, F = 20, V = 12 and E = ?

Using Eucler’s formula, we see

F + V – E = 2

F + V – E = 2

;20 + 12 – E = 2

;32 – E = 2

;E = 32 – 2 = 30

Hence there are 30 edges.

**Question 8.**

Can a polyhedron have 10 faces, 20 edges and 15 vertices?

**Solution :**

If F = 10, V = 15 and E = 20.

Then, we know Using Eucler’s formula,

F + V – E = 2

L.H.S. = F + V – E

= 10 + 15 – 20

= 25 – 20

= 5

R.H.S.; = 2

Hence L.H.S. R.H.S.

Therefore, it does not follow Eucler’s formula.

So polyhedron cannot have 10 faces, 20 edges and 15 vertices.