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CBSE Questions for Class 8 Maths Visualising Solid Shapes Quiz 3 - MCQExams.com
CBSE
Class 8 Maths
Visualising Solid Shapes
Quiz 3
Why is a Rubik's Cube a square prism?
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All of its sides are equal.
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It's smaller than a moving box.
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It's a three-dimensional shape based on at least two squares.
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It's a three-dimensional shape based on at least four squares.
Explanation
Rubik's cube is a 3-D combination which consist of six faces.
All of the faces are squares.
So, we can say at-least two faces are squares.
A square prism
is a three dimensional cuboid figure whose bases are squares.
So, square prism is also based on at-least two squares.
Hence, option C is correct.
Which of the following statements are true?
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A hexagonal prism has two bases that are hexagons.
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A hexagonal prism has six faces that are rectangles.
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Hexagonal prisms that have bases with sides of equal length are called regular hexagonal prisms.
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All of these statements are true.
Explanation
(i) In geometry, the hexagonal prism i
s a prism
with hexagonal
base.
This polyhedron has 8 faces, 18 edges, and 12 vertices.
(ii) Two base faces are hexagon and remaining $$6$$ are square faces.
(iii) Since, any polygon having sides of equal length are called as regular polygon.
Thus, bases with sides of equal length are called as regular hexagonal prisms.
Hence, all three statements are true.
What is a prism?
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Two 2-dimensional shapes joined together to form any enclosed multi-dimensional shape
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Two 2-dimensional shapes joined together to form an enclosed 3-dimensional shape
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Two pentagonal shapes joined together to form an enclosed 3-dimensional shape
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Two circular shapes joined together to form an enclosed 3-dimensional shape
Explanation
A prism
is a polyhedron, with two parallel faces called bases. The other faces are always parallelograms.
It is a $$3$$-dimensional shape having flat faces, identical ends and same cross section.
So, option A is incorrect.
If we join any $$2$$-dimensional shapes, it does not imply that the shape created is a prism.
Circular shapes does not have flat faces in $$3$$-dimensional plane.
If we join two pentagonal shapes, we get a prism.
Hence, option C is correct.
Which of the following is NOT a prism?
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Parallelepiped
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Cuboid
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Cube
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Cylinder
Explanation
Parallelepiped is a three-dimensional shape formed by a $$6$$ parallelogram.
It has identical ends. All faces are flat since all faces of a parallelogram are flat. And has the same cross-section along its length. Therefore it's a prism.
Cuboid is a $$3$$-dimensional shape formed by rectangular faces.
Thus, it has flat faces, identical ends and same cross section along its length.
Cube is also a $$3$$-dimensional shape formed by square faces.
Thus, it has flat faces, identical ends ans same cross section.
But in a cylinder, the faces are not flat.
Only cylinder does not satisfies the properties of prism.
Hence, cylinder is not a prism.
A prism is:
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A set of rectangles with slanted sides
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Two polygons joined together to form an enclosed three-dimensional figure
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A type of box with sides that are not parallel
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Two cylinders with ovals as the top and bottom.
Explanation
The ends of a prism are parallel
and each one is called a base.
A prism is a polyhedron, which means no curves exist and all faces are flat.
A cross section
is the shape made by cutting straight across an object.
Thus, a prism
is a solid object with: identical ends; flat faces; and the same cross section all along its length.
Thus, only option B is correct.
A prism is a solid object with :
I:
identical ends
II: flat faces
III: same cross section all along its length
Which of the following holds true?
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I and II only
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II and III only
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I and III only
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All I, II and III
Explanation
The ends of a prism are parallel
and each one is called a base.
A prism is a polyhedron, which means no curves exist and all faces are flat.
A cross section
is the shape made by cutting straight across an object.
Thus, a prism
is a solid object with: identical ends; flat faces; and the same cross section all along its length
Which of the following has no rectangular faces?
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A triangular pyramid
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A triangular prism
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A square prism
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A cube
Explanation
A triangular prism has $$3$$ rectangular faces and $$2$$ triangular faces.
A square prism
is a three dimensional shape with six rectangular shaped sides
, at least two of which are squares.
Square has all faces rectangular.
All faces of a cube are square and squares has all faces rectangular.
But, a
triangular pyramid has four faces and all four faces are triangular.
Hence, triangular pyramid has no rectangular faces.
A pentagonal prism contains how many pentagons?
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$$1$$
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$$2$$
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$$3$$
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$$5$$
Explanation
The pentagonal prism is
a prism
with a pentagonal
base. It is a type of heptahedron with 7 faces, 15 edges, and 10 vertices.
Thus, a pentagonal prism contains has its two bases as pentagons and other faces are parallelogram.
Hence, it contains $$2$$ pentagons.
Square prisms always consist of at least how many squares?
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$$1$$
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$$2$$
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$$3$$
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$$4$$
Explanation
A square prism
is a three dimensional cuboid figure whose bases are squares. In a square prism
, the opposite sides and angles are congruent.
The bases should be square and there are two bases in each prism.
Hence, it consist of at-least $$2$$ squares.
Faces of the cube are in shape of ..........
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Square
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Rectangle
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Circle
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Triangle
Explanation
Faces of the cube are in the shape of square.
Top view of the triangluar prism will be......
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Square
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Rectangle
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Circle
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Triangle
Explanation
The top-view of a triangular prism is a rectangle.
What shape does the base and the faces of the given figure make?
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Explanation
From the given figure it is clear that the Square and triangle makes the base and face of the figure.
Which of the following answers accurately describes the physical properties of a square pyramid?
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Square base, four triangular sides, six vertices, eight edges
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Square base, four triangular sides, five vertices, eight edges
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Square base, four triangular sides, six vertices, six edges
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Square base, four triangular sides, five vertices, six edges
Explanation
A square pyramid
is a pyramid
with a square
base, four triangular
sides, five vertices, and eight edges.
The base of this pyramid
is a square
, and the top point is the apex. It was mentioned that a square pyramid
is a polyhedron.
Hence, option B is correct.
Prisms are named for:
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The circles that make up the sides
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The rectangles and angles of the shape
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The shapes that form their faces
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The three-dimensional shapes they form
Explanation
We name the prism based on their the faces formed by base.
For example, A prism having square bases is named as square prism.
A prism having pentagon bases are pentagonal prism.
Hence, the prism are named for the shapes that form their faces.
What is the base of the cone?
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Square
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Triangle
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Circle
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None of these
Explanation
The base of cone is a circle.
Base of the rectangular prism is in the form of a ..........
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Square
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Rectangle
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Circle
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Triangle
Explanation
Base of the rectangular prism is in the form of a $$\underline{\text{Rectangle}}.$$
A cylinder has two faces which are ............
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Square
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Circle
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Sphere
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Triangle
Explanation
A cylinder has two circular faces.
In a triangular prism, what is the shape that forms the lateral faces?
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Triangle
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Circle
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Rectangle
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There are no lateral faces
Explanation
Triangular prisms are three-dimensional figures formed by putting rectangles and triangles together.
The bases are triangles. So, the lateral faces are formed by rectangles.
Hence, option C is correct.
When two faces of a triangular prism touch, they form a line segment. What is this line segment called?
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Prism
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Vertex
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Base
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Edge
Explanation
Prism is a three-dimensional figure with two parallel congruent faces, called bases, and lateral faces in the shape of parallelograms.
Vertex - A point where two or more straight lines intersect.
Base - The lowest part of the shape.
Edge - The line segment where two faces meet.
Hence, option D is correct.
Which of the following is the side view of the pyramid?
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Square
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Rectangle
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Circle
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Triangle
Explanation
The side view of a pyramid is a triangle.
Hence, $$Op-D$$ is correct.
How many windows are there in the big room?
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$$1$$
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$$2$$
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$$3$$
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$$4$$
Explanation
This question needs visualisation, the first figure tells us there is one window near the gate and from the second figure it is clear that there are two more windows, so there are total $$3$$ windows.
A polyhedron having a set of four rectangles and two squares is?
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Cube
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Cuboid
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Tetrahedron
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Pyramid
Explanation
Polyhedron having four rectangles and two squares is a cuboid.
In the figure attached $$Height=Width$$
So option $$B$$ is correct.
Euler's formula for polyhedral solids is
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$$N + R = A + 2$$
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$$N + A = R + 2$$
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$$F + V = E + 2$$
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$$F + E = V + 2$$
Explanation
Solution:
Euler's formula for polyhedral solids $$\Longrightarrow F+V=E+2$$
Hence, C is the correct option.
Which of the following is not a polyhedron?
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Cone
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Pyramid
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Prism
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Cylinder
Explanation
Cone is not a polyhedron as it has a curved surface. Similarly cylinder also not a polyhedron.
Which of the following solid object is same as the rectangular prism?
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Cube
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Pyramid
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Cuboid
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None of these
Explanation
A cuboid is also a prism because it has same cross-section along a length. In fact it is a rectangular prism.
Which of the following solid object is same as the square prism?
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Cube
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Pyramid
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Cuboid
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None of these
Explanation
A cube is a square prism.
State whether the following statement true or false:
A rectangular pyramid has 5 rectangular faces.
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True
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False
Explanation
False, rectangular prism has only one rectangular face, rest all are triangles
Which three dimensional figure has $$5$$ faces, $$8$$ edges and $$5$$ vertices?
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Explanation
A) Rectangular Pyramid-It has $$5$$ faces, $$8$$ edges and $$5$$ vertices.
B) Cube- it has $$6$$ faces, $$12$$ edges and $$8$$ vertices.
C)Cuboid-It has $$6$$ faces, $$12$$ edges and $$8$$ vertices.
D) Cylinder-It has $$3$$ faces, $$2$$ edges and no vertices.
Answer : A
Euler's formula is true for all three-dimensional shapes.
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True
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False
Explanation
The given statement is false.
Euler's Formula is only true for polyhedrons. i.e.
$$F + V -E = 2$$
Where, F = Faces and V = Vertices and E = Edges
$$p :$$ The corners of a solid shape are called its edges.
$$q :$$ The line segments of a solid shape are called its vertices.
Which of the following options hold?
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Both $$p$$ and $$q$$ are true
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$$p$$ is true and $$q$$ is false
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Both $$p$$ and $$q$$ are false
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$$p$$ is false and $$q$$ is true
Explanation
Edges are the line segments which make the sides of a solid shape, whereas, vertex is the corner of a solid shape, the point where edges meet.
Hence, both $$p$$ and $$q$$ are false.
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