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Visualising Solid Shapes

Question

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What Euler’s formula? Verify the Euler’s formula for a pentagonal prism.

Solution

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
$rightwards double arrow$ 17 = 17
Which is true, the Euler’s formula is verified.

Some More Questions From Visualising Solid Shapes Chapter

Look at the combination of four cubes as shown in the adjoining figure. Show its various views.

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.

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.

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