Class 8 - Maths - Visualising Solid Shapes

                                                                  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.

              

Answer:

(a)  -----à (iii) ------à (iv)      (b)  -----à (i)- ------à (v)    (c)  -----à (iv) ------à (ii)

(d)  -----à (v) ------à (iii)       (e)  -----à (ii) -------à (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.

                

Answer:

(a) -----à (i) -------Front (ii) -----à Side (iii) -----à Top view

(b) -----à (i) -------Side (ii) ------à Front (iii) -----à Top view

(c) -----à (i) -------Front (ii) -----à Side (iii) -----à Top view

(d) -----à (i) -------Front (ii) -----à Side (iii) -----à Top view

Question 3:

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

                

Answer:

(a) --------à (i) ------àTop view (ii) -------à Front view (iii) --------à Side view

(b) --------à (i) ------àSide view (ii) -------à Front view (iii) --------à Top view

(c) --------à (i) ------àTop view (ii) --------à Side view (iii) ---------à Front view

(d) --------à (i) ------àSide view (ii) -------à Front view (iii) --------à Top view

(e) --------à (i) ------àFront view (ii) -------à Top view (iii) --------à Side view

Question 4:

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

               

 

Answer:

                 

 

 

                                                                  Exercise 10.2

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 –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:

(a) The given map coloured in the required way ia as follows:

 

                                                         

(b) The marks can be put at the given points as follows:

                                                         

(c) The shortest route from the library to bus depot is represented by red colour.

                                                         

(d) Between the market and the city park, the city park is further east.

(e) Between the primary school and Sr. Secondary School, the Sr. Secondary School is further

south.

                                                            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:

(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:

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

Question 3:

Which are prisms among the following:

                          

Answer:

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:

(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:

No, it can be a cuboid also.

Question 6:

Verify Euler’s formula for these solids.

                                      

Answer:

(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:

                                    

Answer:

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:

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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