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Published on: 26/09/2019
Visualising Solid Shapes
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Questions + Answers key
Take MCQ Mathematics Test
1.
What is Euler's formula? Verify the Euler's formula for a pentagonal prism.
2.
How many faces, edges and vertices does a pyramid have with n sided polygon as its base?
3.
Can a polyhedron have V = F = 9 and E = 16. If yes, draw its figure.
4.
A polyhedron has 40 edges and 30 vertices. Find the number of its faces.
5.
The distance between City A and City B on a map is given as 8 cm. If the scale represents 1cm = 200 km, then find the actual distance between City A and City B.
6.
Find the number of faces in the given shapes.
7.
How many vertices does the following solids have?
Sphere
8.
How many faces does the following solids have?
Octagonal pyramid
9.
How many faces does the following solids have?
Hexahedron
10.
Find the number of bases and faces in a Hexagonal pyramid
11.
Find the number of bases and faces in a Rectangular pyramid
12.
Find the number of vertices in a polyhedron which has 30 edges and 12 faces.
13.
A polyhedron has number of vertices equal to \(\frac{3}{2}\) times of number of faces. If polyhedron has 8 edges, then find number of vertices and faces.
14.
Verify which of the following are the faces, edges and, vertices of a polyhedron.
(i) Faces = 10, edges = 20 and vertices = 15
(ii) Faces = 7, edges = 5and vertices = 4
(iii) Faces = 4, edges = 6 and vertices = 4
(iv) Faces= 5, edges = 4 and vertices = 3
15.
Can a polyhedron have 10 faces, 20 edges and 15 vertices?
1.
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.
2.
F = n + 1, V = n + 1 and E = 2 n
3.
Yes, draw an octagonal pyramid.
4.
12
5.
Actual distance represented by
1 cm = 200km
Actual distance represented by 8 cm
= 8 x 200 km = 1600 km
So, actual distance between City A and City B is 1600 km
6.
Number of faces is equal to 16.
7.
In a sphere, there is no vertex.
8.
In an octagonal pyramid, there are 9 faces.
9.
In a hexahedron there are 6 faces
10.
Hexagonal pyramid There is one hexagonal base and six triangular faces in a hexagonal pyramid. The figure shown below is a hexagonal pyramid.
11.
Rectangular pyramid There is one rectangular base and four triangular faces in a rectangular pyramid. The alongside figure is a rectangular pyramid.
12.
For any polyhedron,
F + V - E = 2
Here, F =12, V = ?, E = 30
Using above formula,
12 + V - 30 = 2 ⇒ V - 18 = 2
V = 2 + 18 ⇒ V = 20
13.
Number of faces = 4
Number of vertices = 6
14.
Only option (iii) satisfy F + V = E + 2.
So, it is the required answer.
15.
Given, F = 10, E = 20 and V = 15
By Euler's formula, we have F + V - E = 2
On putting these values in LHS, we get
LHS = F + V - E = 10 +15 - 20 = 25 - 20 = 5 ≠ 2
∴ LHS ≠ RHS
So, Euler's formula is not verified.
Hence, such a polyhedron is not possible.
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