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CBSE Questions for Class 8 Maths Visualising Solid Shapes Quiz 7 - MCQExams.com
CBSE
Class 8 Maths
Visualising Solid Shapes
Quiz 7
The given figure is an example of?
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Cube
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Cuboid
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Tetrahedron
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Prism
Explanation
There are $$4$$ vertices, therefore the given figure is tetrahedron.
Which of the following figures is the solid as viewed from above?
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0%
0%
0%
Explanation
In this figure, base has $$4$$ cubes on either direction and height has $$3$$ cubes.
Only one side is fully covered from front and
$$1$$ side has top level row.
If we see from the top, we will get only boundary of cubes.
Hence, option $$D$$ is correct.
The number of corners, edges, and faces of a cuboid respectively are
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$$8,6,12$$
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$$4,3,6$$
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$$4,4,10$$
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$$8,4,12$$
Explanation
A cuboid has $$8$$ corners/vertices, $$12$$ edges and $$6$$ faces.
Hence, option $$A$$ is correct.
How many faces, edges and vertices respectively does the given solid have?
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$$8, 12, 18$$
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$$10, 18, 12$$
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$$8, 18, 12$$
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$$10, 12, 18$$
Explanation
Number of faces $$= 8$$
Number of edges $$= 18$$
Number of vertices $$= 12$$.
Two positions of a dice are shown below. If the face with $$1$$ dot is at the bottom, then the number of dots on the top face is
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$$2$$
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$$3$$
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$$4$$
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$$5$$
Explanation
Given (Ref. image 1)
Find : Dots on the top when $$1$$ dot is at the bottom.
Solution : By seeing both dices we find two faces have same $$3$$ dots.
So Rearrange the dices dots in clockwise.
Here dots $$3$$ are same and different No. of dots are opposite in Both dices respectively as $$5 \leftrightarrow 6 \, ; \, 4 \leftrightarrow 2$$ so Remaining $$3$$ dots are opposite to $$1$$ dot.
Hence the correct answer is option B.
The Euler's formula for polyhedron is
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$$\displaystyle {V - F + E}=2$$
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$$\displaystyle {V + F - E}=2$$
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$$\displaystyle {V - F - E}=2$$
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$$\displaystyle {V + F - E}=4$$
Number of vertices of a pyramid whose base is a polygon of n-sides.
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$$n$$
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$$n+3$$
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$$n+1$$
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$$n+2$$
How many faces, edges and vertices does the following have and verify using Euler's formula
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$$pentagonal pyramid$$
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$$pentagonal prism$$
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$$square prism$$
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$$square pyramid$$
Explanation
By using Euler's formula :
$$\left( {V - E + F} \right)$$
$$ \Rightarrow 4 - 6 + 4 = 2$$ Polyhexon
$$ \Rightarrow $$ V = Vertices
$$ \Rightarrow $$ E = Edge
and F = Faces
$$ \therefore$$ Pentagonal pyramid has $$(V-E+F=2)$$.
State true or false:
A cylinder has no vertex.
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True
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False
Explanation
The above diagram shows a cylinder. It has $$2$$ curved edges, $$C_1$$ and $$C_2$$, $$2$$ flat faces, $$F_1$$ and $$F_2$$ and $$1$$ curved face. It has no vertex.
Hence, the given statement is true.
The ratio of the number of sides of a square and the number of edges of a cube is
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$$1:2$$
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$$1:3$$
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$$1:4$$
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$$2:3$$
Explanation
Number of sides of square $$=4$$
Edges of cube $$=12$$
$$\therefore$$ Ratio $$=4:12$$
$$\Rightarrow 1:3$$
State whether the following statement are true (T) or false (F):
All the faces of a triangular prism are triangles.
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True
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False
Explanation
False, it has two triangular faces, and two 3 rectangular faces.
State whether the following statement is true (T) or false (F):
All the faces of triangular pyramid are triangles.
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True
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False
Explanation
True, all of the faces of triangular pyramid are triangular. These are 4 in number.
The side faces of a pyramid are:
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Triangles
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Squares
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Polygons
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Trapeziums
Explanation
The sides face of pyramid are triangles.
Hence, (a) is the correct answer.
A cube has 6 faces, 12 edges and 8 vertices.
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True
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False
Explanation
A cube is a 3D object, like shown in the above diagram.
It has $$6$$ square-shaped faces, $$12$$ edges and $$8$$ corners or vertices.
Hence, the given statement is true.
Which of the following will not form a polyhedron ?
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3 triangles
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2 triangles and 3 parallelogram
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8 triangles
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1 pentagon and 5 triangles
Explanation
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 $$(a)$$
Which amongst the following is not a polyhedron ?
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0%
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Explanation
A polyhedron has polygons as its faces. Out of the given options, only cone has a curved face.
Therefore, the correct answer is option $$(c).$$
Which of the following is not a prism ?
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Explanation
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).
Which of the following is the top view of the given shape ?
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Explanation
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.
Which of the following cannot to be true for a polyhedron ?
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V = 4, F = 4, E = 6
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V = 6, F = 8, E = 12
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V = 10, F = 12, E = 20
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V = 4, F = 6, E = 6
Explanation
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 $$D:$$
$$F+V-E=4+6-6=4\neq2$$
We have $$4$$ congruent equilateral triangles. What do we need more to make a pyramid ?
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An equilateral triangle
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A square with same side length as of triangle
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2 equilateral triangles with side length same as triangle.
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2 square with side length same as triangle.
Explanation
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.
In a solid if $$ F=V = 5$$, then the number of edges in this shape is
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6
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4
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8
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2
Explanation
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,
$$ 5 + 5 - E = 2$$
$$\Rightarrow 10 - E = 2$$
$$\Rightarrow E = 8$$
Which of the following is a regular polyhedron ?
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Cuboid
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Triangular prism
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Cube
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Square prism
Explanation
Cuboid, square prism and triangular prism don't have all sides equal.
Only cube has all sides equal, so it has all kind of symmetry and it looks same when seen from all sides.
Shape having only line segments as its edges is a
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Polyhedron
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Cone
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Cylinder
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none of these
Explanation
The correct answer is option $$(a).$$
Because in cone and cylinder edges are circle, which is not a straight ine.
Which of the following can be the base of pyramid ?
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Line segment
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Circle
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Octagon
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Oval
Explanation
A pyramid can have only $$2$$ dimensional polygon as a base and an o
ctagon is a polygon as well as it is a two-dimensional figure. So, an o
ctagon can be the base of a pyramid.
Hence correct answer is option $$C.$$
Which of the following shapes has a vertex:
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Explanation
The correct answer is option $$(c).$$
Because, a vertex is a sharp corner.
Only cone among the given figures has a sharp corner.
A polyhedron can have 3 faces.
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True
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False
Explanation
The given statement is false.
because, tetrahedron is a polyhedron with the minimum number of faces equal to $$4$$.
So, polyhedron cannot have $$3$$ faces.
A polyhedron with least number of faces is known as a triangular pyramid.
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True
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False
Explanation
A polyhedron can have minimum of $$4$$ faces.
And polyhedron with $$4$$ faces is known as tetrahedron or triangular pyramid.
Hence the given statement is true.
Regular octahedron has 8 congruent faces which are isosceles triangles.
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True
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False
Explanation
The given statement is false.
Because, regular octahedron has $$8$$ congruent faces which are all equilateral triangles.
A polyhedron can have 10 faces, 20 edges and 15 vertices.
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True
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False
The number of edges in a parallelogram is 4.
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True
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False
Explanation
The given statement is true as we know a parallelogram is made up of $$4$$ line segments in which we have $$2$$ pairs of parallel lines.
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