Sponsor Area
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?
(b) Do as directed.
(c) Do as directed.
(d) City park.
(e) Senior Secondary school
What happens to F, V and E if some parts are sliced off from a solid? (To start with, you may take a plasticine cube, cut a corner off and investigate).
Case I: The given cuboid has:
(i) Number of faces (F) = 6
(ii) Number of vertices(V) = 8
(iii) Number of edges (E) = 12
We have, F + V = 6 + 8 = 14
F + V - E = 14 - 12 = 2
i.e. F + V - E = 2
or the Euler's formula is verified.
Case II: [A part is sliced off]
We have:
Number of faces (F) = 7
Number of vertices (V) = 10
Number of Edges (E) = 15
Also, F + V = 7 + 10 = 17
and F + V - E = 17 - 15 = 2
Here also, Euler's formula holds true.
Sponsor Area
Since, a prism is a polyhedron having two of its faces congruent and parallel, where as other faces are parallelogram.
∴ (i) No, a nail is not a prism.
(ii) Yes, unsharpened pencil is a prism.
(iii) No, table weight is not a prism.
(iv) Yes, box is a prism.
Here, F = 10, E = 20 and V = 15
We have:
F + V - E = 2
∴ 10 + 15 - 20 = 2
or 25 - 20 = 2
or 5 = 2 which is not true
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Thus, such a polyhedron is not possible.
(i) Polyhedron: A solid shapes bounded by polygons is called a polyhedron. For example, cube, cuboid, etc.
(ii) Prism: A prism is a solid, whose faces are parallelograms and whose ends (or bases) are congruent parallel rectilinear figures.
(iii) Pyramid: A pyramid is a polyhedron whose base is a polygon of any number of sides and whose other faces are triangles with a common vertex.
(i) A cylinder is not a polyhedron.
(ii) A cuboid is a polyhedron.
(iii) A cube is a polyhedron.
(iv) A cone is not a polyhedron.
(v) A sphere is not a polyhedron.
(vi) A pyramid is a polyhedron.
∵ The ends (bases) of the given solid are congruent rectilinear figure each of six sides.
∴ It is a hexagonal prism.
In a hexagonal prism, we have:
The number of faces = 8
The number of edges = 18
The number of vertices = 12
Sponsor Area
If a polyhedron is having number of faces as F, number of edges as E and the number of vertices as V, then the relationship F + V = E + 2 is known as Euler’s formula. Following figure is a solid pentagonal prism.
It has:
Number of faces (F) = 7
Number of edges (E) = 15
Number of vertices (V) = 10
Substituting the values of F, E and V in the relation,
F + V = E + 2
we have
7 + 10 = 15 + 2
17 = 17
Which is true, the Euler’s formula is verified.
Number of vertices (V) = 8
Number of edges (E) = 12
Let the number of faces = V
Now, using the Euler's formula
F + V = E + 2
we have
F + 8 = 12 + 2
F + 8 = 14
F = 14 - 8 
F = 6
Thus, the required number of faces = 6.
Here:
Number of vertices (V) = 20
Number of edges (E) = 30
Let the number of faces are F. Then using Euler's formula, we have
F + V = E + 2 ...(1)
∴ Substituting the values of V and E in (1), we get
F + 20 = 30 + 2
F + 20 = 32
F = 32 - 20
F = 12
Thus, the required number of faces = 12.
Here:
Number of faces (F) = 20
Number of vertices (V) = 12
Let the number of edges be E.
∴ Using Euler's formula, we have
F + V = E + 2
20 + 12 = E + 2 
32 = E + 2
E = 32 - 2 = 30
Thus, the required number of edges = 30.
8 = 8, which is true.
Solution not provided.
Ans. Cuboid;
(i) 8
(ii) 8
(iii) 12
Write the number of
(i) faces
(ii) edges
(iii) vertices for a triangular prism.
Solution not provided.
Ans. (i) 5
(ii) 9
(iii) 6
Solution not provided.
Ans. 5
Solution not provided.
Ans. F + V = E + 2; Four
Solution not provided.
Ans. Square pyramid.
Solution not provided.
Solution not provided.
Solution not provided.
Ans. (a) - (iii); (b) - (iii); (c) - (i); (d) - (iv)
Draw: (i) Its front view.
(ii) Its side view.
(iii) Its top view.
Solution not provided.
Look at the adjoining solid and draw its:
(i) top view.
(ii) front view.
(iii) Side view.
Solution not provided.
B.
A triangleB.
A parallelopipedSponsor Area
Sponsor Area
