saket shishu ranjan higher secondary school vidisha (mp)

SAKET SHISHU RANJAN HIGHER SECONDARY SCHOOL VIDISHA (M.P.)

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CLASS – 8

SUBJECT – MATHEMATICS

CHAPTER – 10

VISUALISING THE SOLID SHAPES

#) 2D Shapes

In geometry, a shape or a figure that has a length and a breadth is a 2D shape. In

other words, a plane object that has only length and breadth is 2 dimensional.

Straight or curved lines make up the sides of this shape. Also, these figures can

have any number of sides. In general, plane figures made of lines are known as

polygons. For example, triangle and square are polygons.

Examples of 2D shapes

Rectangle, circle, square, triangle, quadrilateral and pentagon are some examples of 2D shapes.

#)3D Shapes

In our day to day life, we see several objects around us which have different shapes. For example, books, ball, ice-cream cone etc. One thing common in these objects is that they all have some length, breadth and height or depth. Thus they have three dimensions and so are known as 3D shapes. The D in 3D stands for dimensional. 3D shapes occupy space.


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Examples of 3D Shapes

Cuboid, cube, cylinder, sphere, pyramid and cone are a few examples of 3D shapes

Polyhedron

A solid shape bound by polygons forms a polyhedron. The word polyhedral is the plural of word polyhedron.

Faces : Polygons forming a polyhedron are its faces.

Edges : Line segments common to intersecting faces of a polyhedron are its edges.

Vertices : Points of intersection of edges of a polyhedron are its vertices.

In a polyhedron, three or more edges meet at a point to form a vertex. Some examples of polyhedrons are cuboid, cube, pyramid, and triangular pyramid.

Convex Polyhedron: If the surface of a polyhedron (which consists of its faces, edges, and vertices) does not intersect itself and the line segment connecting any two points of the polyhedron lies within its interior part or surface then such a polyhedron is a convex polyhedron.

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Concave Polyhedron:polyhedron.

Regular polyhedrons : A polyhedron is said to be regular if its faces are made up of regular polygons and the same number of

Prism and pyramid : A prism is a polyhedron whose base and top are congruent polygons and whose other face

On the other hand, a pyramid is a polyhedron whose base is a polygon (of any number of sides ) and whose lateral faces are triangles with a common vertex.

A prism or a pyramid is named after its base. Thus a hexagonahexagon as its base; and a triangular pyramid has a triangle as its base.


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Concave Polyhedron: A non-convex polyhedron is termed as a concave

A polyhedron is said to be regular if its faces are made up of regular polygons and the same number of faces meet at each vertex.

A prism is a polyhedron whose base and top are congruent polygons and whose other faces i.e., lateral faces and parallelograms in the shape.


A prism or a pyramid is named after its base. Thus a hexagonal prismhexagon as its base; and a triangular pyramid has a triangle as its base.

HIGHER SECONDARY SCHOOL VIDISHA (M.P.)

ed as a concave

A polyhedron is said to be regular if its faces are made up faces meet at each vertex.

A prism is a polyhedron whose base and top are congruent faces and parallelograms in the shape.


m has a hexagon as its base; and a triangular pyramid has a triangle as its base.

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3D objects have different views from different positions. A map is different from a picture. A map depicts the location of a particular object/place in relation to o

objects/places. Symbols are used to depict the different objects/places. There is no reference or perspective in a map. Maps involve a scale which is fixed for a particular map. For any polyhedron,

F + V = E + 2

Where ‘F’ stands for number of faces,E stands for number of edges. This relatio

Question 1. For each of the given solid, the two views are given. Match for each solid the corresponding top and front views. The


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3D objects have different views from different positions. A map is different from a picture. A map depicts the location of a particular object/place in relation to o

Symbols are used to depict the different objects/places. There is no reference or perspective in a map. Maps involve a scale which is fixed for a particular map.

Where ‘F’ stands for number of faces, V stands for number of vertices and E stands for number of edges. This relationship is called Euler’s formula

EXERCISE 10.1

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.


A map depicts the location of a particular object/place in relation to other

V stands for number of vertices and nship is called Euler’s formula

For each of the given solid, the two views are given. Match for each first one is done for you.


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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)


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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


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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

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Question 4. Draw the front view, side view and top view of the given objects.

Solution:


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


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

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SAKET SHISHU RANJAN

Question 1. Look at the given map of a city.

Answer the following. (a) Colour the map as follows: Blueyellow-schools, Green-park, Pink(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?

Solution: (a)


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EXERCISE 10.2

Look at the given map of a city.

(a) Colour the map as follows: Blue-water, red- fire station, orangepark, Pink-College, Purple-Hospital, Brown-

(b) Mark a green ‘X’ at the intersection of Road ‘C’ and Nehru Road, Green ‘Y’ at ection 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?


fire station, orange-library, -Cemetery.

(b) Mark a green ‘X’ at the intersection of Road ‘C’ and Nehru Road, Green ‘Y’ at

(c) In red, draw a short street route from Library to the bus depot.

(e) Which is further south, the primary school or the Sr. Secondary School?

SAKET SHISHU RANJAN

(b)

(c)

(d) Between the market and the

(e)Between the primary school school is further south.

Question 2. Draw a map of your classroom using different objects.


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Between the market and the city park, the city park is further east.

school and the sr. secondary school, the sr. secondary

Draw a map of your classroom using proper scale and symbols for


, the city park is further east.

, the sr. secondary

proper scale and symbols for


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Solution: Do your self

Question 3. Draw a map of your school compound using proper scale and symbols for various features like a playground, main building, garden etc.

Solution: Do youself

Question 4. Draw a map giving instructions to your friend so that she reaches your house without any difficulty.

Solution:You can try yourself.

EXERCISE 10.3

Question 1. Can a polyhedron have for its faces (i) 3 triangles? (ii) 4 triangles? (iii) a square and four triangles? Solution: (i) No, such a polyhedron is not possible. A polyhedron has minimum 4 faces.

(ii) Yes, a triangular pyramid has 4 triangular faces.

(iii) Yes, as square pyramid has a square face and four triangular face.


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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.

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) 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.


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Question 5. Is a square prism same as a cube? Explain. Solution: No, It can be a cuboid also.

Question 6. Verify Euler’s formula for these solids.

Solution: (i) Faces = 7 Edges = 15 Vertices = 10 Euler’s formula: F + V = E + 2 ⇒ 7 + 10 = 15 + 2 ⇒ 17 = 17 Hence, Euler’s formula is verified.

(ii) Faces = 9 Edges = 16 Vertices = 9 Euler’s Formula: F + V = E + 2 ⇒ 9 + 9 = 16 + 2 ⇒ 18 = 18 Hence, Euler’s formula is verified.

Question 7. Using Euler’s formula find the unknown.


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Faces ? 5 20

Vertices 6 ? 12

Edges 12 9 ?

Solution: By Euler’s formula, we have

F + V = E + 2

(i)Given : V = 6, E = 12, F = ?

F + 6 = 12 + 2

F = 14 – 6

F = 8

Hence faces = 8

(ii) Given : F = 5, E = 9, V = ?

5 + V = 9 + 2

5 + V = 11

V = 11 – 5

V = 6

Hence vertices = 6

(iii) Given : F = 20, V = 12, E = ?

20 + 12 = E + 2

32 = E + 2

E = 32 – 2

E = 30

Hence edges = 30


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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 + 2 ⇒ 25 ≠ 22 A polyhedron do not have 10 Faces, 20 Edges and 15 Vertices.

saket shishu ranjan higher secondary school vidisha (mp)

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