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Visualising Solid Shapes NCERT Solutions - Class 8 PDF Download

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. 

Visualising Solid Shapes NCERT Solutions - Class 8

Visualising Solid Shapes NCERT Solutions - Class 8

Answer 1: 

Visualising Solid Shapes NCERT Solutions - Class 8

 

Question 2: 

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

Visualising Solid Shapes NCERT Solutions - Class 8

Visualising Solid Shapes NCERT Solutions - Class 8

Visualising Solid Shapes NCERT Solutions - Class 8

Answer 2: 

Visualising Solid Shapes NCERT Solutions - Class 8

Question 3:

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

Visualising Solid Shapes NCERT Solutions - Class 8

Visualising Solid Shapes NCERT Solutions - Class 8

Answer 3: 

Visualising Solid Shapes NCERT Solutions - Class 8

Question 4: 

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

Visualising Solid Shapes NCERT Solutions - Class 8

Answer 4:

Visualising Solid Shapes NCERT Solutions - Class 8

Visualising Solid Shapes NCERT Solutions - Class 8

 

Exercise 10.2 

Question 1: 

Look at the given map of a city. 

Visualising Solid Shapes NCERT Solutions - Class 8

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 – Cementary. 

(b) Mark the 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? 

Answer 1: 

This is a creativity, so do yourself. 

Question 2: 

Draw a map of your class room using proper scale and symbols for different objects. 

Answer 2:

Do yourself.

Question 3: 

Draw a map of your school compound using proper scale and symbols for various features like playground, main building, garden etc. 

Answer 3: 

Do yourself.

Question 4:

Draw a map giving instructions to your friend so that she reaches your house without any difficulty. 

Answer 4: 

Do yourself.

Exercise 10.3 

Question 1: 

Can a polygon have for its faces: 

(i) 3 triangles 

(ii) 4 triangles 

(iii) a square and four triangles 

Answer 1:

(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) 

Answer 2: 

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

Question 3: 

Which are prisms among the following: 

Visualising Solid Shapes NCERT Solutions - Class 8

Answer 3: 

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? 

Answer 4: 

(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. 

Answer 5: 

No, it can be a cuboid also.

Question 6: 

Verify Euler’s formula for these solids. 

Visualising Solid Shapes NCERT Solutions - Class 8

Answer 6: 

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

Using Euler'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 Euler'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.

Question 7: 

Using Euler’s formula, find the unknown: 

Visualising Solid Shapes NCERT Solutions - Class 8

Answer 7: 

In first column,             

F = ?, V = 6 and E = 12

Using Euler'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 Euler'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 Euler'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? 

Answer 8: 

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

Then, we know Using Euler'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 Euler's formula.

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FAQs on Visualising Solid Shapes NCERT Solutions - Class 8

1. What is the importance of visualizing solid shapes in mathematics?
Ans. Visualizing solid shapes is important in mathematics as it helps in understanding and solving problems related to geometry. It allows us to mentally manipulate and analyze different three-dimensional objects, which is crucial for developing spatial reasoning skills.
2. How can visualizing solid shapes help in real-life applications?
Ans. Visualizing solid shapes has various real-life applications. Architects and engineers use it to design buildings, bridges, and other structures. Artists use it to create sculptures and 3D artwork. It also helps in understanding and interpreting maps, blueprints, and other visual representations of objects and spaces.
3. What are the different methods of visualizing solid shapes?
Ans. There are various methods to visualize solid shapes. One method is by using physical models or manipulatives, such as cubes, spheres, and cones. Another method is by using two-dimensional representations, such as drawings or diagrams. Computer software and virtual reality can also be used to visualize and manipulate solid shapes.
4. How can visualizing solid shapes enhance problem-solving skills?
Ans. Visualizing solid shapes enhances problem-solving skills by allowing us to mentally rotate, dissect, and analyze objects. It helps in understanding the relationships between different parts of a shape and visualizing how it can be transformed or manipulated. This spatial reasoning ability is crucial in solving geometry problems and other related mathematical tasks.
5. Are there any online resources or tools available for visualizing solid shapes?
Ans. Yes, there are several online resources and tools available for visualizing solid shapes. Websites and educational platforms offer interactive activities, virtual manipulatives, and simulations that allow students to explore and visualize different three-dimensional objects. Additionally, there are various mobile applications and computer software specifically designed for visualizing and manipulating solid shapes.
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