NCERT Solutions for Class 8 Maths Exercise 10.2

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NCERT Solutions for Class 8 Maths Exercise 10.2 Class 8 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 8 Maths chapter wise NCERT solution for Maths Book all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

NCERT solutions for Class 8 Maths Visualising Solid Shapes Download as PDF

NCERT Solutions for Class 8 Maths Exercise 10.2

NCERT Solutions for Class 8 Maths Visualising Solid Shapes

Class –VIII Mathematics (Ex. 10.2)

NCERT SOLUTION

1. Can a polygon have for its faces:

(i) 3 triangles 

(ii) 4 triangles

(iii) a square and four triangles

Ans. (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.


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.


NCERT Solutions for Class 8 Maths Exercise 10.2

3. Which are prisms among the following:

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


NCERT Solutions for Class 8 Maths Exercise 10.2

4. (i) How are prisms and cylinders alike?

(ii) How are pyramids and cones alike?

Ans. (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.


5. Is a square prism same as a cube? Explain.

Ans. No, it can be a cuboid also.


NCERT Solutions for Class 8 Maths Exercise 10.2

6. Verify Euler’s formula for these solids.

Ans. (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.


NCERT Solutions for Class 8 Maths Exercise 10.2

7. Using Euler’s formula, find the unknown:
Faces?520
Vertices6?12
Edges129?

Ans. 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.


NCERT Solutions for Class 8 Maths Exercise 10.2

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

Ans. 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

 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.

NCERT Solutions for Class 8 Maths Exercise 10.2

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