S.chand Class 8 Maths Solution Chapter 15 Visualising Solid Shapes Exercise 15

 Exercise 15

Question 1

<fig>

1. The adjoining net is made up of two equilateral triangles and three rectangles.

(i) Name the solid it represents.

(ii) How many faces, edges and vertices does this solid have ?

2. For each solid, count the number of faces, vertices and edges. Check if the Euler's rule is true for each one.

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3. Name the solids that have :

(i) 4 faces

(ii) 1 curved surface

(iii) 6 faces

(iv) 5 faces and 5 vertices

(v) 8 triangular faces

(vi) 6 rectangular faces and 2 hexagonal faces.

4. Name the different plane shapes needed to draw the net of:

(i) a cube

(ii) a triangular prism

(iii) a triangular pyramid

(iv) a cylinder

5.Given here is the net of an octahedron with numbers 0 to 7 on the faces.Enlarge these on a cardboard to make a model

(i) How many faces, edges and vertices does this solid have ?

(ii) Check whether Euler's rule is true for the octahedron or not.

6. Draw the 2-D representation of a

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7. On an isometric dotted paper draw the following shapes:

(i) cube

(ii) cuboid

(iii) hexagonal prism

(iv) pentagonal prism

8. Name the solid that would be formed by each net :

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Multiple Choice Questions (MCQs)

9. Which of the following solid shapes has the side

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10. Manya is building prism using straws and balls of clay. How many straws does she need to build a pentagonal prism ?

(a) 18

(b) 15

(c) 20

(d) 13

High Order Thinking Skills (HOTS)

11. How many triangles will the net of hexagonal pyramid contain ?

SChand Composite Mathematics Class 7 Chapter 18 Visualising Solid Shapes Exercise 18C

  Exercise 18 C

Question 1

Name the shape of the cross- section in each solid?

(DIAGRAM TO BE ADDED)

Question 2

What cross- section would you get when you gibe a (a) Vertical cut (b) Horizontal cut  to the following object?

(i) a basket ball

ii) a die

(iii) an unsharpened pencil 

(iv) A 1litre carton of milk 

(v) a joker's cap 

(vi) A chocolate box(triangular 

Question 3

Multiple choice question 

A slice of cheese is cut from the cylinder shaped cheese as shown. What name can be given to the cross-section?

(a) Circle

(b) Square

(c) Rectangle

(d) Triangle

Question 4

Name a three-dimensional figure from which a cross-section of a circle can be made.

(a) Cube

(b) Cuboid

(c) Cone

(d) Pyramid

SChand Composite Mathematics Class 7 Chapter 18 Visualising Solid Shapes Exercise 18B

 Exercise 18B

Question 1

Copy each net into your book and add the face that is needed to make the net of named solid . Shade the added face . 

Prime:- Two parallel congruent Polygonal faced connected  

Pyramid : - Polygon base and triangular faces meet at a common vertex.

(diagram to be added)

Question 2

Label each net as of :

(a) cuboid

(b) cube

(c) triangular pyramid

(d) rectangular pyramid

(e) cone

(f) cylinder

(g) square pyramid

(h) triangular prism

Question 3

Draw the net of a cube. Put the number I to 6 on the faces so that the number  on opposite faces add to 7. Can this be done in more than one. If so, give all ways.

One has been done for you :

(diagram to be added)

Question 4

 Name the different plane shapes needed to draw the net of :

(a) a cube

(b) a triangular prism

(c) a triangular pyramid

(d) a cylinder

(diagram to be added)

Question 5

Which of these nets will not fold up to give a cube?

[Hint. Make the cardboard cutouts of the following nets and fold them to sce whether a cube is formed or not]

(diagram to be added)

Question 6

Only one of these nets could form a pyramid. Which one ?

SChand Composite Mathematics Class 7 Chapter 18 Visualising Solid Shapes Exercise 18A

  Exercise 18 A

Question 1

Leonhard Euler (1707-83) was a famous mathematician who discovered a rule about solids.-He observed the number of faces, vertices and edges of many solids before discovering this rule.

(a) Let us see if you can derive the Euler's rule $(F+V-E=2$ ) by completing the following table.

(Diagram to be added)

Question 2

For each solid, count the number of faces, vertices and edges. Check the Euler's rule for each one.

(Diagram to be added)

(a)  (Diagram to be added)

Sol: F= 7

V=10

E=15

F+V-F=2

17-15=2

(b) (Diagram to be added)

Sol: $F=6$

$V=8$

$E=12$

$F+V-E$

$6+6-12$

$14-12$ = 2

(c)  (Diagram to be added)

Sol: 

$\begin{aligned} F &=7 \\ V &=7 \\ E &=12 \\ 14-12 \\ &=2 \end{aligned}$

(d)  (Diagram to be added)

Sol: $F=9$

$V=9$

$E=16$

$18-16$

$=2$

Question 3

Fill in the blanks. Name a solid that has :

(i) 4 faces                                              

(ii) 4 vertices

(iii) 2 edges

(iv) 6 vertices

(v) No edges.

(vi) 6 faces.

  (Diagram to be added)

Multiple choice question 

Question 4

Which of these solids has the maximum number of vertices ?

(a) Cons

(b) Cylinder

(c) Cuboid

(d) Pyramid

Question 5

If $\mathrm{F}=6$ and $\mathrm{V}=4$, then the value of $\mathrm{E}$ using Euler's formula is

(a) 10

(b) 8

(c) 2

(d) 4