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 Meritnationâ€™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:

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

#### Page No 217:

#### 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:

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

(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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