Rs Aggarwal 2019 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 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 Solutions. All Rs Aggarwal 2019 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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