Rs Aggarwal 2019 2020 Solutions for Class 8 Math Chapter 19 Three Dimensional Figures are provided here with simple step-by-step explanations. These solutions for Three Dimensional Figures are extremely popular among Class 8 students for Math Three Dimensional Figures Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the Rs Aggarwal 2019 2020 Book of Class 8 Math Chapter 19 are provided here for you for free. You will also love the ad-free experience on Meritnation’s Rs Aggarwal 2019 2020 Solutions. All Rs Aggarwal 2019 2020 Solutions for class Class 8 Math are prepared by experts and are 100% accurate.

Page No 215:

Question 1:

Write down the number of faces of each of the following figures:
(i) Cuboid
(ii) Cube
(iii) Triangular prism
(iv) Square pyramid
(v) Tetrahedron

Answer:

(i) A cuboid has 6 faces, namely ABCD, EFGH, HDAE, GCBF, HDCG and EABF.



(ii) A cube has 6 faces, namely IJKL, MNOP, PLIM, OKJN, LKOP and IJNM.


(iii) A triangular prism has 5 faces (3 rectangular faces and 2 triangular faces), namely  QRUT, QTVS, RUVS, QRS and TUV.


(iv) A square pyramid has 5 faces (4 triangular faces and 1 square face), namely OWZ, OWX, OXY, OYZ and WXYZ.


(v) A tetrahedron has 4 triangular faces, namely KLM, KLN, LMN and KMN.

Page No 215:

Question 2:

Write down the number of edges of each of the following figures:
(i) Tetrahedron
(ii) Rectangular pyramid
(iii) cube
(iv) Triangular prism

Answer:

(i) A tetrahedron has 6 edges, namely KL, LM, LN, MN, KN and KM.


(ii) A rectangular pyramid has 8 edges, namely AB, AE, AD, AC, EB, ED, DC and CB.


(iii)  A cube has 12 edges, namely PL, LK, KO, OP, MN, NJ, JI, IM, PM, LI, ON and KJ.


(iv) A triangular prism has 9 edges, namely QR, RS, QS, TU, TV, UV, QT, RU, and SV.

Page No 215:

Question 3:

Write down the number of vertices of each of the following figures:
(i) Cuboid
(ii) Square pyramid
(iii) Tetrahedron
(iv) Triangular prism

Answer:

(i) A cuboid has 8 vertices, namely A, B, C, D, E, F, G and H.


(ii) A square pyramid has 5 vertices, namely O, W, X, Y and Z.


(iii)A tertrahedron has 4 vertices, namely K, L, M and N.


(iv) A triangular prism has 6 vertices, namely Q, R, S, T, U and V.

Page No 215:

Question 4:

Fill in the blanks:
(i) A cube has ....... vertices, ....... edges and ....... faces.
(ii) The point at which three faces of a figure meet is known as its .......
(iii) A cuboid is also known as a rectangular .......
(iv) A triangular pyramid is called a .......

Answer:

(i) A cube has 8 vertices, 12 edges and 6 faces.                   
Vertices: I, J, K, L, M, N, O and P
Edges : IJ, JN, NM, MI, PL, LK, KO, OP, PM, LI, KJ, and ON
Faces : MNJI, POKL, PLIM, OKJN, PONM and LKJI

(ii) The point at which the three faces of a figure meet is known as its vertex.
(iii) A cuboid is also known as a rectangular cube.
(iv) A triangular pyramid is called a tetrahedraon.



Page No 217:

Question 1:

Define Euler's relation between the number of faces, number of edges and number of vertices for various 3-dimensional figures.

Answer:

The Euler's relation for a three dimensional figure can be expressed in the following manner:

F-E+V=2Here,F- Number of facesE-Number of edgesV-Number of vertices

Page No 217:

Question 2:

How many edges are there in a
(i) cuboid
(ii) tetrahedron
(iii) triangular prism
(iv) square pyramid?

Answer:

(i) A cuboid has 12 edges, namely AD, DC, CB, BA, EA, FB, HD, DC, CG, GH, HE, and GF.


(ii) A tetrahedron has 6 edges, namely KL, LM, MN, NL , KM and KN.

(iii) A triangular prism has 9 edges, namely QR, RS, SQ, TU, UV, VT, RU, SV and QT.


(iv) A square pyramid has 8 edges, namely OW, OX, OY , OZ , WX, XY, YZ and ZW.

Page No 217:

Question 3:

How many faces are there in a
(i) cube
(ii) pentagonal
(iii) tetrahedron
(iv) pentagonal pyramid?

Answer:

(i) A cube has 6 faces, namely IJKL, MNOP, PLIM , OKJN, POKL and MNJI.


(ii) A pentagonal prism has 7 faces, i.e. 2 pentagons and 5 rectangles, namely ABCDE, FGHIJ, ABGF, AEJF , EDIJ, DCHI and CBGH.


(iii) A tetrahedron has 4 faces, namely KLM, KLN, LMN and KMN.


(iv) A pentagonal pyramid has 6 faces, i.e. 1 pentagon and 5 triangles, namely NOPQM, SNM, SOP, SNO, SMQ and  SQP.

Page No 217:

Question 4:

How many vertices are there in a
(i) cuboid
(ii) tetrahedron
(iii) pentagonal prism
(iv) square pyramid?

Answer:

(i) A cuboid has 8 vertices, namely A, B, C, D, E, F, G and H.


(ii) A tetrahedron has 4 vertices, namely K, L, M and N.


(iii) A pentagonal prism has 10 vertices, namely A, B, C, D, E, F, G, H, I and J.


(iv) A square pyramid has 5 vertices, namely O, W, X, Y and Z.

Page No 217:

Question 5:

Verify Euler's relation for each of the following:
(i) A square
(ii) A tetrahedron
(iii) A triangular prism
(iv) A square pyramid

Answer:

Euler's relation is:

F-E+V=2Here:F- Number of facesE-Number of edgesV-Number of vertices

(i) A square prism  

(There is an error in this question. It should have been a square prism rather than square.)                                        

Number of faces = F=2 squares+4 rectangular=6Number of edges = E = 12Number of vertices =V= 8F-E+V=6-12+8=2

(ii) A tetrahedron

Number of faces = F=4Number of edges = E = 6Number of vertices =V= 4F-E+V=4-6+4=2

(iii) A triangular prism

Number of faces = F=2 triangular + 3 rectangular = 5Number of edges = E = 9 Number of vertices =V =6F-E+V=5-9+6=2

(iv) A square pyramid

Number of faces = F=2 triangular + 3 rectangular = 5Number of edges = E = 8Number of vertices =V =5F-E+V=5-8+5=2



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