Rs Aggarwal 2019 2020 Solutions for Class 8 Maths 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 Maths 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 Maths Chapter 19 are provided here for you for free. You will also love the ad-free experience on Meritnationâ€™s Rs Aggarwal 2019 2020 Solutions. All Rs Aggarwal 2019 2020 Solutions for class Class 8 Maths are prepared by experts and are 100% accurate.

#### Page No 215:

#### 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:

#### 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:

#### 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:

#### 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:

#### Answer:

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

$F-E+V=2\phantom{\rule{0ex}{0ex}}H\mathrm{ere},\phantom{\rule{0ex}{0ex}}F-\mathrm{Number}\mathrm{of}\mathrm{faces}\phantom{\rule{0ex}{0ex}}E-\hspace{0.17em}\mathrm{Number}\mathrm{of}\mathrm{edges}\phantom{\rule{0ex}{0ex}}V-\hspace{0.17em}\mathrm{Number}\mathrm{of}\mathrm{vertices}$

#### Page No 217:

#### 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:

#### 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:

#### 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:

#### Answer:

Euler's relation is:

$F-E+V=2\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}Here:\phantom{\rule{0ex}{0ex}}F-\mathrm{Number}\mathrm{of}\mathrm{faces}\phantom{\rule{0ex}{0ex}}E-\hspace{0.17em}\mathrm{Number}\mathrm{of}\mathrm{edges}\phantom{\rule{0ex}{0ex}}V-\hspace{0.17em}\mathrm{Number}\mathrm{of}\mathrm{vertices}$

(i) A square prism

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

$\mathrm{Number}\mathrm{of}\mathrm{faces}=F=2\mathrm{squares}+4\mathrm{rectangular}=6\phantom{\rule{0ex}{0ex}}\mathrm{Number}\mathrm{of}\mathrm{edges}=E=12\phantom{\rule{0ex}{0ex}}\mathrm{Number}\mathrm{of}\mathrm{vertices}=V=8\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow \left(F-E+V\right)=6-12+8=2$

(ii) A tetrahedron

$\mathrm{Number}\mathrm{of}\mathrm{faces}=F=4\phantom{\rule{0ex}{0ex}}\mathrm{Number}\mathrm{of}\mathrm{edges}=E=6\phantom{\rule{0ex}{0ex}}\mathrm{Number}\mathrm{of}\mathrm{vertices}=V=4\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow \left(F-E+V\right)=4-6+4=2$

(iii) A triangular prism

$\mathrm{Number}\mathrm{of}\mathrm{faces}=F=2\mathrm{triangular}+3\mathrm{rectangular}=5\phantom{\rule{0ex}{0ex}}\mathrm{Number}\mathrm{of}\mathrm{edges}=E=9\phantom{\rule{0ex}{0ex}}\mathrm{Number}\mathrm{of}\mathrm{vertices}=V=6\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow \left(F-E+V\right)=5-9+6=2$

(iv) A square pyramid

$\mathrm{Number}\mathrm{of}\mathrm{faces}=F=2\mathrm{triangular}+3\mathrm{rectangular}=5\phantom{\rule{0ex}{0ex}}\mathrm{Number}\mathrm{of}\mathrm{edges}=E=8\phantom{\rule{0ex}{0ex}}\mathrm{Number}\mathrm{of}\mathrm{vertices}=V=5\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\Rightarrow \left(F-E+V\right)=5-8+5=2$

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