NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes Ex 10.3
NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid
Shapes Ex 10.3 are the part of NCERT Solutions for Class 8 Maths. Here you can
find the NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes
Ex 10.3.
Ex 10.3 Class 8 Maths Question 1.
Can a polyhedron have for its faces(i) 3 triangles?
(ii) 4 triangles?
(iii) a square and four triangles?
Solution:
(i) No,
because polyhedron must have edges meeting at vertices which are points.
(ii) Yes, because all the edges are meeting at
the vertices. For example, a tetrahedron.
Ex 10.3 Class 8 Maths Question 2.
Is it possible to have a polyhedron with any given number of faces?(Hint: Think of a pyramid)
Solution:
Yes, it is possible if the number of faces is greater than or equal to 4.
For example: Tetrahedron or triangular pyramid which has 4 faces.
Ex 10.3 Class 8 Maths Question 3.
Which are prisms among the following?Solution:
(ii) Unsharpened pencil and (iv) A box are the prisms.
Ex 10.3 Class 8 Maths Question 4.
(i) How are prisms and cylinders alike?(ii) How are pyramids and cones alike?
Solution:
(i) If the number of sides of the base in a prism is
increased to a certain extent, then the prism will take the shape of a cylinder.
(ii) If the number of sides of the base in a pyramid is increased to a certain
extent, then the pyramid will take the shape of a cone.
Ex 10.3 Class 8 Maths Question 5.
Is a square prism same as a cube? Explain.Solution:
A cube is a square prism but every square prism
cannot be cube. A square prism may be a cuboid also.
Ex 10.3 Class 8 Maths Question 6.
Verify Euler’s formula for these solids.Solution:
(i) Faces = 7
Sides = 15
Vertices = 10
Verification of Euler’s formula: F + V – E = 2
⇒ 7 + 10 – 15 = 2
⇒ 2 = 2
Hence, Euler’s formula is verified.
(ii) Faces
= 9
Sides = 16
Vertices = 9
Verification of Euler’s formula: F + V – E = 2
⇒ 9 + 9 – 16
= 2
⇒ 2 = 2
Hence, Euler’s formula is verified.
Ex 10.3 Class 8 Maths Question 7.
Using Euler’s formula find the unknown.
Faces |
? |
5 |
20 |
Vertices |
6 |
? |
12 |
Edges |
12 |
9 |
? |
Solution:
Using Euler’s Formula: F + V – E = 2
Faces |
8 |
5 |
20 |
Vertices |
6 |
6 |
12 |
Edges |
12 |
9 |
30 |
Ex 10.3 Class 8 Maths Question 8.
Can a polyhedron have 10 faces, 20 edges and 15 vertices?Solution:
Here, faces
(F) = 10, edges (E) = 20, vertices (V) = 15
According to Euler’s Formula:
F + V – E = 2
⇒ 10 + 15 –
20 = 25 – 20
⇒ 5 ≠ 2
Therefore, a polyhedron do not have 10 faces, 20 edges and 15 vertices.
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