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Visualising Solid Shapes

Question

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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).

Solution

Consider the following cuboid ABCDEFGH:

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.

Some More Questions From Visualising Solid Shapes Chapter

In the figure, a brick is given. Draw its front view, side view and top view.

Following solids are made by joining cubes. Draw their different views.

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-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?

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

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

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

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).

Can a polyhedron have for its faces 3 triangles?

Can a polyhedron have for its faces 4 triangles?

Can a polyhedron have for its faces a square and four triangles?

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