Visualising Solid Shapes Test

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Visualising Solid Shapes Test - 23

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following will not form a polyhedron ?

A
3 triangles

B
2 triangles and 3 parallelogram

C
8 triangles

D
1 pentagon and 5 triangles

Solution

The smallest polyhedron possible is a tetrahedron with four triangular faces.
Hence polyhedron can't be formed by 3 triangles.
The correct answer is option $$(a)$$
Question 2
1 / -0

Which of the following can be the base of pyramid ?

A
Line segment

B
Circle

C
Octagon

D
Oval

Solution

A pyramid can have only $$2$$ dimensional polygon as a base and an octagon is a polygon as well as it is a two-dimensional figure. So, an octagon can be the base of a pyramid.

Hence correct answer is option $$C.$$
Question 3
1 / -0

Which of the following is the top view of the given shape ?

A

B

C

D

Solution

The correct answer is option $$(d).$$
When, seen from top we see $$1$$ square from $$1^{st}$$ row with diamond on it, and $$2$$ blank squares from $$2^{nd}$$ row.
Question 4
1 / -0

Which of the following is not a prism ?

A

B

C

D

Solution

Because, a prism has a solid shape consisting of two equal ends, flat faces or surfaces and identical cross-section across its length.
$$A$$, $$C$$ and $$D$$ have two ends as square, triangle and pentagon respectively and their cross-section throughout is same.
So, option $$B$$ which is not a three dimensional figure is only non prism figure given.
The correct answer is option (b).
Question 5
1 / -0

We have $$4$$ congruent equilateral triangles. What do we need more to make a pyramid ?

A
An equilateral triangle

B
A square with same side length as of triangle

C
2 equilateral triangles with side length same as triangle.

D
2 square with side length same as triangle.

Solution

The correct answer is option $$(b).$$
Because, pyramid has a polygon base, so we require a square.and on each edge of polygon there lies a triangle.
We have $$4$$ equilateral triangles, so we need polygon with all $$4$$ sides equal.
So, we must take square.
And as triangle lies on edges of square, so its side must be equal to side of triangle.
Question 6
1 / -0

In a solid if $$ F=V = 5$$, then the number of edges in this shape is

A
6

B
4

C
8

D
2

Solution

The correct answer is option $$(c).$$
For any polyhedron, Euler' s formula ;
$$F + V - E = 2$$
Where, $$F$$ = Face and $$V$$ = Vertices and $$E$$ = Edges
Given, $$ F = V = 5$$
On putting the values of $$F$$ and $$V$$ in the about formulae,
$$ 5 + 5 - E = 2$$
$$\Rightarrow 10 - E = 2$$
$$\Rightarrow E = 8$$
Question 7
1 / -0

Which of the following cannot to be true for a polyhedron ?

A
V = 4, F = 4, E = 6

B
V = 6, F = 8, E = 12

C
V = 10, F = 12, E = 20

D
V = 4, F = 6, E = 6

Solution

The correct answer is option $$(d)$$.
Euler's Formula for any polyhedron$$ = F + V -E = 2$$
Where, F = Faces and V = Vertices and $$E =$$ Edges
Option $$A:$$
$$F+V-E=4+4-6=2$$

Option $$B:$$
$$F+V-E=6+8-12=2$$

Option $$C:$$
$$F+V-E=10+12-20=2$$

Option $$D:$$
$$F+V-E=4+6-6=4\neq2$$
Question 8
1 / -0

Shape having only line segments as its edges is a

A
Polyhedron

B
Cone

C
Cylinder

D
none of these

Solution

The correct answer is option $$(a).$$
Because in cone and cylinder edges are circle, which is not a straight ine.
Question 9
1 / -0

Which of the following shapes has a vertex:

A

B

C

D

Solution

The correct answer is option $$(c).$$
Because, a vertex is a sharp corner.
Only cone among the given figures has a sharp corner.
Question 10
1 / -0

The side faces of a pyramid are:

A
Triangles

B
Squares

C
Polygons

D
Trapeziums

Solution

The sides face of pyramid are triangles.
Hence, (a) is the correct answer.