NCERT Solutions Maths Ch-10 Visualising Solid Shapes for Class 8th
Here’s a summary of key concepts and solutions for Chapter 10 “Visualising Solid Shapes” from NCERT Class 8 Maths:
3D Shapes: Understanding solids like cubes, cuboids, cylinders, cones, and spheres.
Views of 3D Shapes:
- Front View: What you see when looking from the front.
- Top View: What you see when looking from above.
- Side View: What you see from the side.
Net of Solid Shapes: A 2D representation of a 3D shape that can be folded to form the shape.
Volume and Surface Area: Introduction to calculating the volume and surface area of simple solids.
NCERT Solutions of Class 8th Chapter 10 Visualising Solid Shapes Ex 10.1, 10.2 and 10.3
We try to teach you all Questions in easy way. We solve all chapter wise sums of maths textbook. In every chapter include NCERT solutions. For solutions of Exercise 10.1, 10.2 and 10.3
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) A bottle → (iii) → (iv)
(b) A weight → (i) → (v)
(c) A flask → (iv) → (ii)
(d) Cup and saucer → (v) → (iii)
(e) Container → (ii) → (i)
Question 2.
For each of the given solid, the three views are given. Identify for each solid the corresponding top, front and side views.
Solution:
(a) An Almirah → (i) Front → (ii) Side → (iii) Top
(b) A Match box → (i) Side → (it) Front → (iii) Top
(c) A Television → (i) Front → (ii) Side → (iii) Top
(d) A Car → (i) Front → (ii) Side → (iii) Top
Question 3.
For each given solid, identify the top view, front view and side view.
Solution:
(a) (i) Top → (ii) Front → (iii) Side
(b) (i) Side → (ii) Front → (iii) Top
(c) (i) Top → (ii) Side → (iii) Front
(d) (i) Side → (ii) Front → (iii) Top
(e) (i) Front → (ii) Top → (iii) Side
Question 4.
Draw the front view, side view and top view of the given objects.
Solution:
Question 1.
Look at the given map of a city.
Answer the following.
(a) Colour the map as follows: Blue-water, red- fire station, orange-library, yellow-schools, Green-park, Pink-College, Purple-Hospital, Brown-Cemetery.
(b) Mark a green ‘X’ at the intersection of Road ‘C’ and Nehru Road, Green ‘Y’ at the intersection of Gandhi Road and Road A.
(c) In red, draw a short street route from Library to the bus depot.
(d) Which is further east, the city park or the market?
(e) Which is further south, the primary school or the Sr. Secondary School?
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.
(iii) Yes, because all the eight edges meet at the vertices.
Question 2.
Is it possible to have a polyhedron with any given number of faces?
(Hint: Think of a pyramid)
Solution:
Pyramid
Yes, it is possible if the number of faces is greater than or equal to 4.
Example: Pyramid which has 4 faces.
Question 3.
Which are prisms among the following?
Solution:
Only (ii) unsharpened pencil and (iv) a box are the prism.
Question 4.
(i) How are prisms and cylinders alike?
(ii) How are pyramids and cones alike?
Solution:
(i) If the number of sides in a prism is increased to certain extent, then the prism will take the shape of cylinder.
(ii) If the number of sides of the pyramid is increased to same extent, then the pyramid becomes a cone.
Question 5.
Is a square prism same as a cube? Explain.
Solution:
Every square prism cannot be cube. It may be cuboid also.
Question 6.
Verify Euler’s formula for these solids.
Solution:
(i) Faces = 7
Sides = 15
Vertices = 10
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
Euler’s Formula: F + V – E = 2
⇒ 9 + 9 – 16 = 2
⇒ 2 = 2
Hence, Euler’s formula is verified.
Question 7.
Using Euler’s formula find the unknown.
| Faces | ? | 5 | 20 |
| Vertices | 6 | ? | 12 |
| Edges | 12 | 9 | ? |
Solution:
| Faces | 8 | 5 | 20 |
| Vertices | 6 | 6 | 12 |
| Edges | 12 | 9 | 30 |
Using Eulers Formula: F + V – E = 2
Question 8.
Can a polyhedron have 10 faces, 20 edges and 15 vertices?
Solution:
Here faces = 10, Edges = 20, Vertices = 15
According to Euler’s Formula:
F + V – E = 2
⇒ 10 + 15 – 20 = 25 – 20
⇒ 5 ≠ 2
A polyhedron do not have 10 Faces, 20 Edges and 15 Vertices.