# Visualizing 3 D In 2 D

Chapters

- ap-scert-8th-class-Maths-Lesson-1-Rational-Numbers
- ap-scert-8th-class-Maths-Lesson-4-Exponents-and-Powers
- ap-scert-8th-class-Maths-Lesson-10-Direct-and-Inverse-Proportions
- ap-scert-8th-class-Maths-Lesson-2-Linear-Equations-in-One-Variable
- ap-scert-8th-class-Maths-Lesson-3-Construction-of-Quadrilaterals
- ap-scert-8th-class-Maths-Lesson-6-Square-Roots-and-Cube-Roots
- ap-scert-8th-class-Maths-Lesson-7-Frequency-Distribution-Tables-and-Graphs
- ap-scert-8th-class-Maths-Lesson-8-Exploring-Geometrical-Figures
- ap-scert-8th-class-Maths-Lesson-9-Area-of-Plane-Figures
- ap-scert-8th-class-Maths-Lesson-11-Algebraic-Expressions
- ap-scert-8th-class-Maths-Lesson-12-Factorisation
- ap-scert-8th-class-Maths-Lesson-13-Visualizing-3-D-in-2-D
- ap-scert-8th-class-Maths-Lesson-14-Surface-Areas-and-Volume-(Cube-Cuboid)
- ap-scert-8th-class-Maths-Lesson-15-Playing-with-Numbers

- ap-scert-8th-class-Maths-Lesson-1-Rational-Numbers
- ap-scert-8th-class-Maths-Lesson-4-Exponents-and-Powers
- ap-scert-8th-class-Maths-Lesson-10-Direct-and-Inverse-Proportions
- ap-scert-8th-class-Maths-Lesson-2-Linear-Equations-in-One-Variable
- ap-scert-8th-class-Maths-Lesson-3-Construction-of-Quadrilaterals
- ap-scert-8th-class-Maths-Lesson-6-Square-Roots-and-Cube-Roots
- ap-scert-8th-class-Maths-Lesson-7-Frequency-Distribution-Tables-and-Graphs
- ap-scert-8th-class-Maths-Lesson-8-Exploring-Geometrical-Figures
- ap-scert-8th-class-Maths-Lesson-9-Area-of-Plane-Figures
- ap-scert-8th-class-Maths-Lesson-11-Algebraic-Expressions
- ap-scert-8th-class-Maths-Lesson-12-Factorisation
- ap-scert-8th-class-Maths-Lesson-13-Visualizing-3-D-in-2-D
- ap-scert-8th-class-Maths-Lesson-14-Surface-Areas-and-Volume-(Cube-Cuboid)
- ap-scert-8th-class-Maths-Lesson-15-Playing-with-Numbers

- Solutions
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Solutions

Draw the following 3-D figures on isometric dot sheet.

Solution

Draw a cuboid on the isometric dot sheet with the measurements 5 units × 3 units × 2 units.

Solution:

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 |

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. |

Consider the distance between two consecutive dots to be 1 cm and draw the front view, side view and top view of the following 3-D figures.

Solution

Count the number of faces , vertices , and edges of given polyhedra and verify Euler’s formula.

Solution

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.

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.

Can a polyhedra have 4 triangular faces only? explain.

Solution:

Yes, a triangular pyramid have 4 triangular faces.

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

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.

Complete the following table

Solution

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

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.

(ii) Answer the following questions.

- (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

PDF Download

Question Papers

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