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.