myhelper: RS Aggarwal solution class 8 chapter 19 Three Dimensional Figure Exercise 19B

Exercise 19B

Page-217

Q1 | Ex-19B | Class 8 | RS AGGARWAL | chapter 19 | Three Dimensional Figure

Question 1:

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

Answer 1:

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

$F - E + V = 2 H ere, F - Number of faces E - Number of edges V - Number of vertices$

Q2 | Ex-19B | Class 8 | RS AGGARWAL | chapter 19 | Three Dimensional Figure

Question 2:

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

Answer 2:

(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.

Q3 | Ex-19B | Class 8 | RS AGGARWAL | chapter 19 | Three Dimensional Figure

Question 3:

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

Answer 3:

(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.

Q4 | Ex-19B | Class 8 | RS AGGARWAL | chapter 19 | Three Dimensional Figure

Question 4:

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

Answer 4:

(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.

Q5 | Ex-19B | Class 8 | RS AGGARWAL | chapter 19 | Three Dimensional Figure

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 5:

Euler's relation is:

$F - E + V = 2 H e r e : F - Number of faces E - Number of edges V - Number of vertices$

(i) A square prism

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

$Number of faces = F = 2 squares + 4 rectangular = 6 Number of edges = E = 12 Number of vertices = V = 8 \Rightarrow (F - E + V) = 6 - 12 + 8 = 2$

(ii) A tetrahedron

$Number of faces = F = 4 Number of edges = E = 6 Number of vertices = V = 4 \Rightarrow (F - E + V) = 4 - 6 + 4 = 2$

(iii) A triangular prism

$Number of faces = F = 2 triangular + 3 rectangular = 5 Number of edges = E = 9 Number of vertices = V = 6 \Rightarrow (F - E + V) = 5 - 9 + 6 = 2$

(iv) A square pyramid

$Number of faces = F = 2 triangular + 3 rectangular = 5 Number of edges = E = 8 Number of vertices = V = 5 \Rightarrow (F - E + V) = 5 - 8 + 5 = 2$

RS Aggarwal solution class 8 chapter 19 Three Dimensional Figure Exercise 19B

Exercise 19B

Page-217

Q1 | Ex-19B | Class 8 | RS AGGARWAL | chapter 19 | Three Dimensional Figure

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Question 1:

Answer 1:

Q2 | Ex-19B | Class 8 | RS AGGARWAL | chapter 19 | Three Dimensional Figure

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Question 2:

Answer 2:

Q3 | Ex-19B | Class 8 | RS AGGARWAL | chapter 19 | Three Dimensional Figure

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Answer 3:

Q4 | Ex-19B | Class 8 | RS AGGARWAL | chapter 19 | Three Dimensional Figure

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Question 4:

Answer 4:

Q5 | Ex-19B | Class 8 | RS AGGARWAL | chapter 19 | Three Dimensional Figure

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