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.
Answer:
(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.
Answer:
(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)
Answer:
(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?
Answer:
(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?
Answer:
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
Answer:
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?
Answer:
(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.
Answer:
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.
Answer:
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?
Answer:
No
Solution:
For any polyhedron, we have, F + V – E = 2
Hence, LHS = 10 + 15 – 20 = 25 – 20 = 5
Hence, LHS ≠ RHS
This is not verified from Euler’s formula.