Edudel, Directorate of Education Govt. of NCT of Delhi Class 8 Mental Maths Question Bank Chapter 9 Visualising Solid Shapes Questions Solution. In this chapter, there are total 40 math problems. We have given each questions solution step by step.
Edudel Class 8 Mental Maths Chapter 9 Visualising Solid Shapes:
Identify the polyhedron whose nets are given below:
ANSWER:
From given figure, polyhedron is Square pyramid.
ANSWER:
ANSWER:
From given figure, polyhedron is Triangular prism.
ANSWER:
ANSWER:
From given figure, polyhedron is Hexagonal Pyramid
ANSWER:
From given figure, polyhedron is Tetrahedron
ANSWER:
From given figure, polyhedron is Cuboid
ANSWER:
From given figure, polyhedron is Cube.
7.) Following are the combinations of a polyhedron. Find the missing part to make the combination true for a polyhedron.
i.) 4 faces, 4 vertices, ______ edges.
ANSWER:
We know,
Euler’s formula for a polyhedron is: F+V-E=2
Where ‘F’ stands for number of faces
‘V’ stands for number of vertices,
‘E’ stands for number of edges.
F = 4, V = 4
F+V-E=2
4 + 4 -E=2
E = 8 – 2
E = 6
To make polyhedron, the true combination are 4 faces, 4 vertices, 6 edges.
ii.) _______ faces, 20 vertices, 30 edges.
ANSWER:
We know,
Euler’s formula for a polyhedron is: F+V-E=2
Where ‘F’ stands for number of faces
‘V’ stands for number of vertices,
‘E’ stands for number of edges.
E = 30, V = 20
F+V-E=2
F + 20- 30=2
F – 10 = 2
F = 12
To make polyhedron, the true combination are12 faces, 20 vertices, 30 edges.
iii.) 20 faces, _______ vertices, 54 edges.
ANSWER:
We know,
Euler’s formula for a polyhedron is: F+V-E=2
Where ‘F’ stands for number of faces
‘V’ stands for number of vertices,
‘E’ stands for number of edges.
F = 20, E = 54
F+V-E=2
20 + V – 54=2
-34+ V = 2
V = 36
To make polyhedron, the true combination are 20 faces, 36 vertices, 54 edges.
iv.) 14 faces, 24 vertices, _______ edges.
ANSWER:
We know,
Euler’s formula for a polyhedron is: F+V-E=2
Where ‘F’ stands for number of faces
‘V’ stands for number of vertices,
‘E’ stands for number of edges.
F = 14, V = 24
F+V-E=2
14 + 24 -E=2
E = 38 – 2
E = 36
To make polyhedron, the true combination are 14 faces, 24 vertices,36 edges.
8.) What is the other name for a triangular pyramid having congruent equilateral triangles as faces?
ANSWER:
The other name for a triangular pyramid having congruent equilateral triangles as faces is Tetrahedron.
9.) What is the other name of a quadrilateral prism square base?
ANSWER:
the other name of a quadrilateral prism square base is cuboid.
10.) What is the special name of a polyhedron whose base is a polygon and whose lateral faces are triangles with a common vertex?
ANSWER:
the special name of a polyhedron whose base is a polygon and whose lateral faces are triangles with a common vertex is Pyramid.
11)
Find the number of squares visible in the top view, the side view and the front view of the following solids:
ANSWER:
From given figure we see number of squares from,
Top View = 6
Side View = 2
Front View = 4
ANSWER:
From given figure we see number of squares from,
Top View = 6
Side View = 3
Front View = 4
ANSWER:
From given figure we see number of squares from,
Top View = 5
Side View = 2
Front View = 4
ANSWER:
From given figure we see number of squares from,
Top View = 3
Side View = 4
Front View = 6
ANSWER:
From given figure we see number of squares from,
Top View = 1
Side View = 1
Front View = 1
ANSWER:
From given figure we see number of squares from,
Top View = 2
Side View = 3
Front View = 4
17.) Find the number of faces in a prism with a pentagonal base.
ANSWER:
Here, we have to find Number of faces in a prism with a pentagonal base.
We know,
In prism, Number of faces = n + 2
Where, n = number of sides of the base
n = 5 (pentagonal base.)
Number of faces = n + 2
Number of faces = 5 + 2 = 7
Number of faces in a prism with a pentagonal base is 7.
18.) Find the number of edges in a pyramid with a pentagonal base.
ANSWER:
Here, we have to find number of edges in a pyramid with a pentagonal base.
We know,
In a pyramid, number of edges = 2n
Where, n = number of sides of the base
n = 5 (pentagonal base.)
Number of edges = 2n
Number of edges = 2 x 5 = 10
Number of edges in a pyramid with a pentagonal base is 10.
19.) Find the number of vertices in a triangular prism.
ANSWER:
Here, we have to find number of vertices in a triangular prism.
We know,
In prism, Number of vertices = 2n
Where, n = number of sides of the base
n = 3 (triangular prism.)
Number of vertices = 2 x 3
Number of vertices = 6
Number of vertices in a triangular prism is 6.
20.) Find the number of faces in a pyramid with pentagonal base.
ANSWER:
Here, we have to find number of Faces in a pyramid with a pentagonal base.
We know,
In a pyramid, number of faces = n + 1
Where, n = number of sides of the base
n = 5 (pentagonal base.)
Number of faces = 5 + 1
Number of faces = 6
Number of faces in a pyramid with a pentagonal base is 6.
21.) Find the number of edges in a prism with a pentagonal base.
ANSWER:
Here, we have to find number of edges in a prism with a pentagonal base.
We know,
In a prism, number of edges = 3n
Where, n = number of sides of the base
n = 5 (pentagonal base.)
Number of edges = 3n
Number of edges = 3 x 5 = 15
Number of edges in a prism with a pentagonal base is 15.
22.) Find the number of edges in a triangular pyramid.
ANSWER:
Here, we have to find number of edges in a triangular pyramid.
We know,
In a triangular pyramid, number of edges = 2n
Where, n = number of sides of the base
n = 3 (triangular pyramid)
Number of edges = 2n
Number of edges = 2 x 3 = 6
Number of edges in a triangular pyramid is 6.
23.) Find the number of faces in a prism with a square base.
ANSWER:
Here, we have to find Number of faces in a prism with a square base.
We know,
In prism, Number of faces = n + 2
Where, n = number of sides of the base
n = 4 (square base)
Number of faces = n + 2
Number of faces = 4 + 2 = 6
Number of faces in a prism with a pentagonal base is 6.
24.) Find the number of faces in the given figure.
ANSWER:
We have to find number of faces in a given cube.
Given figure is cube with 1 additional face.
The cube has 6 faces.
The given figure has 6 + 1 = 7 faces.
25.) Find the number of edges in the given figure.
ANSWER:
We have to find number of edges in the given figure.
The given figure is Pyramid with a square base.
Pyramid with a square base has 8 number of edges.
The given figure has 8 edges.
26.) Find the number of vertices in the given figure.
ANSWER:
We have to find the number of vertices in the given figure.
The given figure is Prism with a rectangular base (Cuboid)
Prism with a rectangular base (Cuboid) has 8 number of vertices.
The given figure has 8 number of vertices.
27.) What do we call the polygons forming a polyhedron?
ANSWER:
The polygons forming a polyhedron is called as “Faces of polyhedron”
28.) Find the odd one out:
Matchbox, Chalk box, Book, Coin, Sugar cubes, Dice
ANSWER:
Given items are cuboid shape except coin.
The odd one out is coin.
29.) Find the odd one out:
Ball, Sun, Earth, Circle, Moon, football, Bangle
ANSWER:
Given items are sphere shape except circle which is 2D.
The odd one out is Circle.
30.) Find the number of edges in the given figure.
ANSWER:
We have to find number of edges in the given figure.
Given figure is combination of Pyramid with a square base and Prism with a rectangular base (Cuboid).
Pyramid with a square base has 8 edges.
Prism with a rectangular base (Cuboid) has 12 edges.
There are 4 edges which are common in between two.
Number of edges in the given figure = (8 + 12) – 4
Number of edges in the given figure = 16
31.) Which 3-D shape is obtained on making a pile of 50 coins of the same size?
ANSWER:
From making a pile of 50 coins of the same size we get shape of “Right circular cylinder.”
32.) What is the minimum number of faces that a polyhedron can have?
ANSWER:
The minimum number of faces that a polyhedron can have is 4.
- ) A polyhedron has 6 edges and 4 faces. Find the number of its vertices.
ANSWER:
Given that, polyhedron has 6 edges and 4 faces.
We have to find the number of vertices.
We know,
Euler’s formula for a polyhedron is: F+V-E=2
Where ‘F’ stands for number of faces
‘V’ stands for number of vertices,
‘E’ stands for number of edges.
F = 4, E = 6
F+V-E=2
4 + V – 6=2
-2+ V = 2
V = 4
The number of vertices is 4.
34.) A polyhedron has 7 vertices and 12 edges. Find the number of its faces.
ANSWER:
Given that, polyhedron has 7 vertices and 12 edges.
We have to find number of faces.
We know,
Euler’s formula for a polyhedron is: F+V-E=2
Where ‘F’ stands for number of faces
‘V’ stands for number of vertices,
‘E’ stands for number of edges.
E = 12, V = 7
F+V-E=2
F + 7 – 12=2
F – 5 = 2
F = 7
Number of faces = 7
35.) Find the number of cuboids measuring 5 cm×3 cm ×2 cm required to form a solid cube of edge 30 cm.
ANSWER:
Given that,
Solid cube of edge 30 cm.
Measurement of cuboid is 5 cm × 3 cm × 2 cm
We know,
Volume of Cube = (edge) 3
Volume of cuboid = Length x Breadth x Height
The number of cuboids = Volume of Cube / Volume of cuboid
The number of cuboids = 30 x 30 x 30 / 5 cm × 3 cm × 2 cm
The number of cuboids = 900
36.) Find the number of unit cubes required to form a solid cuboid measuring 5 unit × 4 units ×3 units.
ANSWER:
Given that,
Measurement of cuboid is 5 unit × 4 units ×3 units.
We have to find the number of unit cubes
We know,
Volume of Cube = (edge) 3
Volume of cuboid = Length x Breadth x Height
The number of unit cube = Volume of cuboid
The number of unit cube = 5 unit × 4 units ×3 units.
The number of unit cube = 60
37.) Find the number of edges in the given figure.
ANSWER:
We have to find the number of edges in the given figure.
Given figure is Prism with a hexagonal base.
Number of edges in Prism with a hexagonal base = 3n
‘n’ is the number of sides of the base
n = 6 (hexagonal base)
Number of edges in Prism with a hexagonal base = 3n
Number of edges in Prism with a hexagonal base = 3 x 6 = 18
Number of edges in Prism with a hexagonal base is 18.
38.) Find the number of cubes required to make the adjacent 3D shape in figure.
ANSWER:
The number of cubes required to make the adjacent 3D shape in figure is 10.
39.) Find the number of edges in a triangular prism.
ANSWER:
We have to find the number of edges in a triangular prism.
Here, we have to find number of edges in a triangularprism
We know,
In a triangularprism, number of edges = 3n
Where, n = number of sides of the base
n = 3 (triangularbase.)
Number of edges = 3n
Number of edges = 3 x 3 = 9
Number of edges in a triangularprism is 9.
40.) Find the number of faces in a pyramid with a triangle as its base.
ANSWER:
Here, we have to find number of Faces in a pyramid with a Triangular base.
We know,
In a pyramid, number of faces = n + 1
Where, n = number of sides of the base
n = 3 (Triangular base.)
Number of faces = 3+ 1
Number of faces = 4
Number of faces in a pyramid with a Triangular base is 4.
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