Chapters

Share

Solutions

Solution

Solution:

##### Question 3. Find the number of unit cubes in the following 3-D figures.

Solution:

 Figure No. of cubes i) 2 + 3 = 5 ii) 2 × 4 + 1 = 9 iii) 4 + 16 = 20 iv 1 + 4 + 9 = 14
##### Question 4. Find the areas of the shaded regions of the 3-D figures given in question number 3.

Solution:

 Figure Area of the shaped regions i) 3 × 1 × 1 =3 Sq. Units. ii) 4(2 × 1) + 1 = 9 Sq. Units. iii) 4 + (16 - 8) = 4 + 8= 12 Sq. Units. iv) 1 + (4 - 1) ÷ (9 - 4) = 1 + 3 + 5 = 9 Sq.Units.

Solution

Solution

##### Question 2. Is a square prism and cube are same? explain.

Solution:
All cubes are square prisms, but converse is not true. (i.e.,) All square prisms are either cubes or, not.

##### Question 3. Can a polyhedra have 3 triangular faces only? explain.

Solution:
Any polyhedra can’t have 3 triangular faces because the triangular pyramids are formed starts with 4 faces. So it does not exist.

##### Question 4. Can a polyhedra have 4 triangular faces only? explain.

Solution:
Yes, a triangular pyramid have 4 triangular faces.

##### Question 5. Complete the table by using Euler’s formula.
 F 8 5 ? V 6 ? 12 E ? 9 30

Solution:

 F 8 5 20 V 6 6 12 E 12 9 30

i) E = V + F- 2 = 8 + 6- 2 = 12
ii) V = E + 2- F = 9 + 2- 5 = 6
iii) F = E + 2- V = 30 + 2-12 = 20

##### Question 6. Can a polyhedra have 10 faces ,20 edges and 15 vertices?

Solution:
No. of faces = 10
No. of edges = 20
No. of vertices = 15
According to Euler’s formula E = V + F – 2
⇒ 20 = 15 + 10 - 2
20 = 25 - 2
20 = 23 (False)
∴ A polyhedra doesn’t exist with 10 faces, 20 edges, 15 vertices.

Solution

##### Question 8. Name the 3-D objects or shapes that can be formed from the following nets.
• (i) Hexagonal pyramid
• (ii) Cuboid
• (iii) Pentagonal pyramid
• (iv) Cylinder
• (v) Cube
• (vi) Hexagonal pyramid
• (vii) Trapezoid
##### Question 9. Draw the following diagram on the check ruled book and fmd out which of the following diagrams makes cube? (i)

Solution:
The diagrams which makes cubes are a, b, c, e.

• (a) Name the polyhedron which has four vertices, four faces’?
• (b) Name the solid object which has no vertex?
• (c) Name the polyhedron which has 12 edges’?
• (d) Name the solid object which has one surface’?
• (e) How a cube is different from cuboid?
• (f) Which two shapes have same number of edges, vertices and faces?
• (g) Name the polyhedron which has 5 vertices and 5 faces’?

Solution:

• (a) Tetrahedron
• (b) Sphere
• (c) Cube/Cuboid
• (d) Sphere
• (e) Cube is a regular polyhedron where cuboid is not.
• (f) Cube, Cuboid
• (g) Square pyramid

(iii) Write the names of the objects given below

Solution:

• (a) Octagonal prism
• (b) Hexagonal prism
• (c) Triangular prism
• (d) Pentagonal prism