RS Aggarwal 2019 Solutions for Class 8 Math Chapter 19 - Three Dimensional Figures

Question 1:

Question 2:

(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.

Question 3:

(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.

Question 4:

(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.

Question 1:

(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.

Question 2:

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

$$\begin{gathered} F-E+V=2 \\ H\mathrm{ere}, \\ F- \mathrm{Number} \mathrm{of} \mathrm{faces} \\ E-\hspace{0.17em}\mathrm{Number} \mathrm{of} \mathrm{edges} \\ V-\hspace{0.17em}\mathrm{Number} \mathrm{of} \mathrm{vertices} \end{gathered}$$

Question 3:

(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.

Question 4:

(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.

Question 5:

(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.