Visualising Solid Shapes Class-8 ML Aggarwal ICSE Maths
Visualising Solid Shapes Class-8 ML Aggarwal ICSE Maths Solutions Chapter-17. We provide step by step Solutions of Exercise / lesson-17 Visualising Solid Shapes Class-8th ML Aggarwal ICSE Mathematics.
Our Solutions contain all type Questions with Exe-17.1 , Exe-17.2, Objective Type Questions (including Mental Maths Multiple Choice Questions, HOTS ), and Check Your Progress to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-8 Mathematics.
Visualising Solid Shapes Class-8 ML Aggarwal ICSE Maths Solutions Chapter-17
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Objective Type Questions,
Multiple Choice Questions ,(MCQ)
Ex 17.1, Visualising Solid Shapes Class-8 ML Aggarwal ICSE Maths Solutions
Question 1.
Match the objects with their shapes:
Answer
(i) A tent – (g) A cone surmounted on a cylinder.
(ii) A tin – (f) A cylindrical shell.
(iii) A bowl – (b) A hemispherical shell.
(iv) An agricultural field – (a) A triangular field adjoining a square field.
(v) A groove – (h) A cone took out of a cylinder.
(vi) A toy – (d) A hemisphere surmounted on a cone.
(vii) A circular park – (e) A circular path around a circular ground.
(viii) Across path – (c) Two rectangular cross paths inside a rectangular park.
Question 2.
For each of the given solid, the two views are given. Match for each solid the corresponding front and top views.
Answer
Question 3.
For the given solid, identify the front, side and top views and write it in the space provided.
Answer
Question 4.
For each of the given solid, the three views are given. Identify for each solid the corresponding top, front and side views.
Answer
Object Different views
(a) An Inkpot
(i) Front
(ii) Side
(iii) Top
(b) A gas stove
(i) Front
(ii) Top
(iii) Side
(c) A brick
(i) Top
(ii) Front
(iii) Side
(d) A container
(i) Front
(ii) Side
(iii) Top
(e) Almirah
(i) Side
(ii) Top
(iii) Front
(f) A matchbox
(i) Side
(ii) Front
(iii) Top
Question 5.
For each given solid, identify the top view, front view and side view.
Answer
(a)
(i) Top view
(ii) Side view
(iii) Front view
(b)
(i) Side view
(ii) Front view
(iii) Top view
(i) Top view
(ii) Side view
(iii) Front view
(d)
(i) Side view
(ii) Front view
(iii) Top view
(e)
(i) Front view
(ii) Top view
(iii) Side view
Question 6.
Draw the front view, side view and top view of the given objects:
Answer
Visualising Solid Shapes Class-8 ML Aggarwal ICSE Maths Solutions , Ex 17.2
Question 1.
Can a polyhedron have for its faces
(i) 3 triangles?
(ii) 4 triangles?
(iii) a square and four triangles?
Answer
(i) No
(ii) Yes
(iii) Yes
Question 2.
Which are prisms among the following?
Answer
Prisms are only (i) and (iv).
Question 3.
Verify Euler’s formula for these solids:
Answer
Question 4.
Can a polyhedron have 15 faces, 30 edges and 20 vertices?
Answer
Can a polyhedron have 15 faces, 30 edges and 20 vertices.
∵ F + V = E + 2
⇒ 15 + 20 = 35 and 30 + 2 = 32
∵ 35 ≠ 32
∴ It has not.
Question 5.
If a polyhedron has 8 faces and 8 vertices, find the number of edges.
Answer
A polyhedron has 8 faces and 8 vertices.
∴ Number of edges = F + V – 2 = 8 + 8 – 2 = 14
Question 6.
If a polyhedron has 7 faces and 10 vertices, find the number of edges.
Answer
A polyhedron has 7 faces and 10 vertices.
∴ Number of edges = F + V – 2 = 7 + 10 – 2 = 15
Question 7.
Write the number of faces, vertices and edges in
(i) an octagonal prism
(ii) decagonal pyramid.
Answer
Question 8.
Using Euler’s formula, complete the following table:
Answer
Objective Type Questions, Visualising Solid Shapes Class-8 ML Aggarwal ICSE Maths Solutions Chapter-17
Mental Maths
Question 1.
Fill in the blanks:
(i) A solid made up of polygonal regions is called ………
(ii) Polyhedrons which are not convex are called ………
(iii) A polyhedron is said to be ……… if all of its faces are regular polygons and the same number of faces meet at each vertex.
(iv) A polyhedron whose base and top are congruent polygons and whose lateral faces are parallelograms in shape is called a ………
(v) A prism whose base and top are congruent hexagon is called a ………
(vi) A polyhedron whose all lateral faces are triangles is called a ………
(vii) A triangular pyramid is also known as ………
(viii) A rectangular prism is also known as ………
(ix) The polygonal regions forming a polyhedron are called ………
Answer
(i) A solid made up of polygonal regions is called polyhedron.
(ii) Polyhedrons which are not convex are called concave polyhedron.
(iii) A polyhedron is said to be regular polyhedron if all of its faces are
regular polygons and the same number of faces meet at each vertex.
(iv) A polyhedron whose base and top are congruent polygons and
whose lateral faces are parallelograms in shape is called a prism.
(v) A prism whose base and top are congruent hexagon is called a hexagonal prism.
(vi) A polyhedron whose all lateral faces are triangles is called a triangular pyramid.
(vii) A triangular pyramid is also known as a tetrahedron.
(viii) A rectangular prism is also known as a cuboid.
(ix) The polygonal regions forming a polyhedron are called faces.
Question 2.
State which of the following statements are true (T) or false (F):
(i) A cylinder is a polyhedron.
(ii) All the prisms and pyramids are polyhedrons.
(iii) A tetrahedron is the only pyramid which can be a regular polyhedron.
(iv) The line segments where the faces of a polyhedron meet are called edges.
(v) F + E = V + 2 is called a Euler’s formula.
(vi) In any prism number of faces is 2 more than number of sides of polygonal base.
(vii) In any pyramid number of edges is twice the number of sides of polygonal base.
(viii) An octagonal prism has 18 vertices.
(ix) All pyramids are prisms.
(x) Lateral faces of a pyramid are triangles.
Answer
(i) A cylinder is a polyhedron. False
(ii) All the prisms and pyramids are polyhedrons. True
(iii) A tetrahedron is the only pyramid
which can be a regular polyhedron. True
(iv) The line segments where the faces of
a polyhedron meet are called edges. True
(v) F + E = V + 2 is called a Euler’s formula. False
Correct:
It is F + V = E + 2.
(vi) In any prism number of faces is 2 more than
the number of sides of polygonal base. True
(vii) In any pyramid number of edges is twice
the number of sides of polygonal base. True
(viii) An octagonal prism has 18 vertices. False Correct:
It has 8 + 8 = 16
(ix) All pyramids are prisms. False
Correct:
Both are different shapes.
(x) Lateral faces of a pyramid are triangles. True
Multiple Choice Questions
MCQs, Visualising Solid Shapes Class-8 ML Aggarwal ICSE Maths Solutions Chapter-17
Choose the correct answer from the given four options (3 to 17):
Question 3.
Which of the following is not a 2-dimensional shape?
(a) Triangle
(b) Circle
(c) Sphere
(d) Rectangle
Answer
Sphere is not a two-dimensional shape, (c)
Question 4.
Which of the following is a 3-dimensional shape?
(a) Parallelogram
(b) Cylinder
(c) Square
(d) none of these
Answer
Cylinder is a 3-dimensional shape. (b)
Question 5.
Name the pyramid shown in the given figure.
(a) Nonagonal pyramid
(b) Octagonal pyramid
(c) Decagonal pyramid
(d) Hexagonal pyramid
Answer
Octagonal pyramid. (b)
Question 6.
How many parallel and congruent faces does a cylinder have?
(a) 4
(b) 3
(c) 2
(d) none
Answer
A cylinder has two parallel and congruent faces. (c)
Question 7.
How many pairs of congruent parallel faces does a rectangular prism have?
(a) 8
(b) 6
(c) 4
(d) 3
Answer
A rectangular prism has 3 pairs of congruent
and parallel faces. (d)
Question 8.
How many congruent isosceles triangle does a square pyramid have?
(a) 2
(b) 4
(c) 6
(d) 8
Answer
A square pyramid has 4 congruent isosceles triangles. (b)
Question 9.
Which amongst the following is not a polyhedron?
Answer
Figure (c) is not a polyhedron. (c)
Question 10.
Which of the following is not a prism?
Answer
Figure (b) is not a prism. (b)
Question 11.
The number of triangular faces of a triangular prism are
(a) 2
(b) 3
(c) 4
(d) 5
Answer
A triangular prism has 2 triangular faces, (a)
Question 12.
The number of edges in a pentagonal pyramid are
(a) 5
(b) 10
(c) 15
(d) 20
Answer
A pentagonal pyramid has 10 edges. (b)
Question 13.
The number of rectangular faces in a hexagonal prism are
(a) 6
(b) 8
(c) 10
(d) 12
Answer
A hexagonal prism has 6 rectangular faces. (a)
Question 14.
In a polyhedron E = 15, V = 10, then F is
(a) 3
(b) 5
(c) 7
(d) 9
Answer
E = 15, V = 10
F + V = E + 2
⇒ F = E + 2 – V = 15 + 2 – 10 = 7 (c)
Question 15.
In a polyhedron F = 5, E = 8, then V is
(a) 3
(b) 5
(c) 7
(d) 9
Answer
F + V = E + 2
So ⇒ 5 + V = 8 + 2
or ⇒ 5 + V = 10
Hence⇒ V = 10 – 5 = 5 (b)
Question 16.
In a polyhedron F = 17, V = 30, then E is
(a) 30
(b) 45
(c) 60
(d) none of these
Answer
F = 17, V = 30
F + V = E + 2
⇒ E = F + V – 2
⇒ E = 17 + 30 – 2 = 45 (b)
Question 17.
A polyhedron have 4 faces, 4 vertices and 6 edges. Name the polyhedron.
(a) A rectangular prism
(b) A triangular prism
(c) A rectangular pyramid
(d) A triangular pyramid
Answer
A polyhedron has 4 faces, 4 vertices and 6 edges.
∴ It is triangular pyramid. (d)
Higher Order Thinking Skills
HOTS , Visualising Solid Shapes Class-8 ML Aggarwal ICSE Maths Solutions Chapter-17
Question 1.
Which of the following nets can be folded to form a cone?
Answer
Net in figure (3) can be folded to form a cone.
Question 2.
Which of the following nets can be folded to form a cylinder?
Answer
Net in the figure (1) and (2) can be folded to form a cylinder.
Check Your Progress
Visualising Solid Shapes Class-8 ML Aggarwal ICSE Maths Solutions Chapter-17
Question 1.
Write the number of faces, vertices and edges of a
(i) hexagonal pyramid
(ii) octagonal pyramid
(iii) decagonal pyramid
(iv) nonagonal pyramid
(v) heptagonal prism
(vi) decagonal prism.
Answer
Faces | Vertices | Edges | |
(i) hexagonal pyramid | 7 | 7 | 12 |
(ii) octagonal pyramid | 9 | 9 | 16 |
(iii) decagonal pyramid | 11 | 11 | 20 |
(iv) nonagonal pyramid | 10 | 10 | 18 |
(v) heptagonal prism | 9 | 14 | 21 |
(vi) decagonal prism | 12 | 20 | 30 |
Question 2.
Give three examples of 3-dimensional shapes around you which are the combinations of 2 or more 3-dimensional shapes.
Answer
3-dimensional shapes which are the combination of
2 or more 3-dimensional shapes.
(i) A funnel: Combination of cone and cylinder.
(ii) A toy: Combination of a cone and hemisphere.
(iii) An ice-cream cone: Combination of a cone and hemisphere.
(iv) A circus tent: Combination of a cylinder and a cone.
Question 3.
Give two examples of solids which are not polyhedrons.
Answer
Sides which are not polyhedron:
(i) Cylinder
(ii) Sphere
(iii) Cone
Question 4.
Why a pentagonal pyramid having all its edges congruent cannot be a regular polyhedron?
Answer
A pentagonal pyramid having all its edges congruent cannot be a regular
polyhedron because all the vertices of it are not formed by the same number of faces.
Question 5.
In a polyhedron, if F = 8 and V = 12 then find the number of edges.
Answer
In a polyhedron,
F = 8, V = 12, then edges
F + V = E + 2
⇒ E = F + V- 2
⇒ Edges = 8 + 12 – 2 = 18
Question 6.
Verify Euler’s formula for the following figures:
Answer
Question 7.
For each of the given solid, the three views are given. Identify for each solid the corresponding top, front and side views:
Answer
(a) A television
(i) Front view
(ii) Side view
(iii) Top view
(b) An aeroplane
(i) Front view
(ii) Side view
(iii) Top view
(c) A prism
(i) Top view
(ii) Front view
(iii) Side view
(d) A car
(i) Front view
(ii) Side view
(iii) Top view
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