Three-Dimensional Figures | Mathematics (Maths) Class 8 PDF Download

 Page 1


Q u e s t i o n : 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
S o l u t i o n :
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 3rectangularfacesand2triangularfaces
, namely  QRUT, QTVS, RUVS, QRS and TUV.
iv
A square pyramid has 5 faces 4triangularfacesand1squareface
, namely OWZ, OWX, OXY, OYZ and WXYZ. 
v
A tetrahedron has 4 triangular faces, namely KLM, KLN, LMN and KMN.
Page 2


Q u e s t i o n : 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
S o l u t i o n :
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 3rectangularfacesand2triangularfaces
, namely  QRUT, QTVS, RUVS, QRS and TUV.
iv
A square pyramid has 5 faces 4triangularfacesand1squareface
, namely OWZ, OWX, OXY, OYZ and WXYZ. 
v
A tetrahedron has 4 triangular faces, namely KLM, KLN, LMN and KMN.
Q u e s t i o n : 2
Write down the number of edges of each of the following figures:
i
Tetrahedron
ii
Rectangular pyramid
iii
cube
iv
Triangular prism
S o l u t i o n :
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. 
Q u e s t i o n : 3
Write down the number of vertices of each of the following figures:
i
Cuboid
ii
Page 3


Q u e s t i o n : 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
S o l u t i o n :
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 3rectangularfacesand2triangularfaces
, namely  QRUT, QTVS, RUVS, QRS and TUV.
iv
A square pyramid has 5 faces 4triangularfacesand1squareface
, namely OWZ, OWX, OXY, OYZ and WXYZ. 
v
A tetrahedron has 4 triangular faces, namely KLM, KLN, LMN and KMN.
Q u e s t i o n : 2
Write down the number of edges of each of the following figures:
i
Tetrahedron
ii
Rectangular pyramid
iii
cube
iv
Triangular prism
S o l u t i o n :
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. 
Q u e s t i o n : 3
Write down the number of vertices of each of the following figures:
i
Cuboid
ii
Square pyramid
iii
Tetrahedron
iv
Triangular prism
S o l u t i o n :
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.
Q u e s t i o n : 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 .......
S o l u t i o n :
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
Page 4


Q u e s t i o n : 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
S o l u t i o n :
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 3rectangularfacesand2triangularfaces
, namely  QRUT, QTVS, RUVS, QRS and TUV.
iv
A square pyramid has 5 faces 4triangularfacesand1squareface
, namely OWZ, OWX, OXY, OYZ and WXYZ. 
v
A tetrahedron has 4 triangular faces, namely KLM, KLN, LMN and KMN.
Q u e s t i o n : 2
Write down the number of edges of each of the following figures:
i
Tetrahedron
ii
Rectangular pyramid
iii
cube
iv
Triangular prism
S o l u t i o n :
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. 
Q u e s t i o n : 3
Write down the number of vertices of each of the following figures:
i
Cuboid
ii
Square pyramid
iii
Tetrahedron
iv
Triangular prism
S o l u t i o n :
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.
Q u e s t i o n : 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 .......
S o l u t i o n :
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.
Q u e s t i o n : 5
Define Euler's relation between the number of faces, number of edges and number of vertices for various 3-dimensional figures.
S o l u t i o n :
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
Q u e s t i o n : 6
How many edges are there in a
i
cuboid
ii
tetrahedron
iii
triangular prism
iv
square pyramid?
S o l u t i o n :
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 5


Q u e s t i o n : 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
S o l u t i o n :
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 3rectangularfacesand2triangularfaces
, namely  QRUT, QTVS, RUVS, QRS and TUV.
iv
A square pyramid has 5 faces 4triangularfacesand1squareface
, namely OWZ, OWX, OXY, OYZ and WXYZ. 
v
A tetrahedron has 4 triangular faces, namely KLM, KLN, LMN and KMN.
Q u e s t i o n : 2
Write down the number of edges of each of the following figures:
i
Tetrahedron
ii
Rectangular pyramid
iii
cube
iv
Triangular prism
S o l u t i o n :
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. 
Q u e s t i o n : 3
Write down the number of vertices of each of the following figures:
i
Cuboid
ii
Square pyramid
iii
Tetrahedron
iv
Triangular prism
S o l u t i o n :
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.
Q u e s t i o n : 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 .......
S o l u t i o n :
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.
Q u e s t i o n : 5
Define Euler's relation between the number of faces, number of edges and number of vertices for various 3-dimensional figures.
S o l u t i o n :
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
Q u e s t i o n : 6
How many edges are there in a
i
cuboid
ii
tetrahedron
iii
triangular prism
iv
square pyramid?
S o l u t i o n :
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.
Q u e s t i o n : 7
How many faces are there in a
i
cube
ii
pentagonal
iii
tetrahedron
iv
pentagonal pyramid?
S o l u t i o n :
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.