Lesson: Visualising Solid Shapes
Exercise 10.1
Question 1
For each of the given solid, the two views are given. Match for each solid the
corresponding top and front views. The first one is done for you.
(a) (iii) (iv), (b) (i) (v), (c) (iv) (ii), (d) (v) (iii),
(e) (ii) (i)
Solution:
(a) (iii) (iv), (b) (i) (v), (c) (iv) (ii), (d) (v) (iii),
(e) (ii) (i)
Question 2
For each of the given solid, the three views are given. Identify for each solid the
corresponding top, front and side views.
(a) (i) Front (ii) Side (iii) Top (b) (i) Side (ii) Front (iii) Top
(c) (i) Front (ii) Side (iii) Top (d) (i) Front (ii) Side (iii) Top
Solution:
(a) (i) Front, (ii) Side, (iii) Top, (b) (i) Side, (ii) Front, (iii) Top,
(c) (i) Front, (ii) Side, (iii) Top, (d) (i) Front, (ii) Side, (iii) Top
Question 3
For each given solid, identify the top view, front view and side view.
(a)
(a) (i) Top, (ii) Front, (iii) Side, (b) (i) Side, (ii) Front, (iii) Top
(c) (i) Top, (ii) Side, (iii) Front, (d) (i) Side, (ii) Front, (iii) Top
(e) (i) Front, (ii) Top, (iii) Side
Solution:
Question 4
Draw the front view, side view and top view of the given objects.
Solution:
Exercise 10.3
Question 1
Can a polyhedron have for its faces?
(i) 3 triangles? (ii) 4 triangles? (iii) A square and four triangles?
(i) No (ii) Yes (iii) Yes
Solution:
(i) No (ii) Yes (iii) Yes
Question 2
Is it possible to have a polyhedron with any given number of faces?
Possible, only if the numbers of faces are greater than or equal to 4
Solution:
Possible, only if the numbers of faces are greater than or equal to 4.
Question 3
Which are prisms among the following?
A nail Unsharpened pencil A table weight A box
Only (ii) and (iv)
Solution:
Only (ii), and (iv)
Question 4
(i) How are prisms and cylinders alike?
(ii) How are pyramids and cones alike?
(i) A prism becomes a cylinder as the number of sides of its base becomes larger
and larger.
(ii) A pyramid becomes a cone as the number of sides of its base becomes larger
and larger.
Solution:
(i) A prism becomes a cylinder as the number of sides of its base becomes
larger and larger.
(ii) A pyramid becomes a cone as the number of sides of its base becomes
larger and larger.
Question 5
Is a square prism same as a cube?
Explain.
No. It can be a cuboid also
Solution:
No. It can be a cuboid also
Question 6
Verify Euler’s formula for these solids.
Solution:
F + V E = 2
This relationship is called Euler’s formula.
Where, F = Number of faces, V = Number of vertices, E = Number of edges.
(i) Here, F = 7, V = 10, E = 15
From Euler’s formula, F + V E = 2
LHS = 7 + 10 15 = 17 15 = 2 = RHS
Hence, verified the Euler’s formula,
(ii) Here, F = 9, V = 9, E = 16
From Euler formula, F + V E = 2
LHS = 9 + 9 8 = 18 16 = 2 = RHS
Hence Euler’s formula is verified.
Question 7
Using Euler’s formula finds the unknown.
Faces 8, Vertices 6, Edges 30
Solution:
F + V E = 2
(i) F = 2 + E V = 2 + 12 6 = 14 6 = 8
(ii) V = 2 + E F = 2 + 9 5 = 11 5 = 6
(iii) E = F + V 2 = 20 + 12 2 = 32 2 = 30
Question 8
Can polyhedron have 10 faces, 20 edges and 15 vertices?