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Visualising Solid Shapes

Question

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A dodecahedron is having 20 vertices and 30 edges. How many faces are there?

Solution

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
$rightwards double arrow$ F + 20 = 32
$rightwards double arrow$ F = 32 - 20
$rightwards double arrow$ F = 12
Thus, the required number of faces = 12.

Some More Questions From Visualising Solid Shapes Chapter

For each of the given solid, the three views are given. Identify for each solid the corresponding top, front and side views.

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

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

Look at the hut and draw its front view, side view and the top view.

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.

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