Write down the number of faces of each of the following figures:
A. Cuboid
B. Cube
C. Triangular prism
D. Square pyramid
E. Tetrahedron
A. 6
Face is also known as sides. A Cuboid has six faces.
Book, Matchbox, Brick etc. are examples of Cuboid.
B.6
A Cube has six faces and all faces are equal in length.
Sugar Cubes, Dice etc. are examples of Cube.
C. 5
A Triangular prism has two triangular faces and three rectangular faces.
D. 5
A Square pyramid has one square face as a base and four triangular faces as the sides. So, Square pyramid has total five faces.
E. 4
A Tetrahedron (Triangular Pyramid) has one triangular face as a base and three triangular faces as the sides. So, Tetrahedron has total four faces.
Write down the number of edges of each of the following figures:
A. Tetrahedron
B. Rectangular pyramid
C. Cube
D. Triangular prism
A. 6
A Tetrahedron has six edges.
OA, OB, OC, AB, AC, BC are the 6 edges.
B. 8
A Rectangular Pyramid has eight edges.
AB, BC, CD, DA, OA, OB, DC, OD are the 8 edges.
C. 12
A Cube has twelve edges.
AB, BC, CD, DA, EF, FG, GH, HE, AE, DH, BF, CG are the edges.
D. 9
A Triangular prism has nine edges.
AB, BC, CA, DE, EF, FD, AD, BE, CF are the9 edges.
Write down the number of vertices of each of the following figures:
A. Cuboid
B. Square pyramid
C. Tetrahedron
D. Triangular prism
A. 8
A Cuboid has eight vertices.
A, B, C, D, E, F, G, H are the 8 vertices.
B. 5
A Square Pyramid has five vertices.
O, A, B, C, D are the 5 vertices.
C. 4
A Tetrahedron has four vertices.
O, A, B, C are the vertices.
D. 6
A Triangular prism has six vertices.
A, B, C, D, E, F are the vertices.
Fill in the blanks:
A. A cube has……… vertices, ………….edges and …………..faces.
B. The point at which three faces of a figure meet is known as its…………
C. A cuboid is also known as a rectangular…………..
D. A triangular pyramid is called a..………….
A. 8, 12, 6
A Cube has 8 vertices, 12 edges and 6 faces.
A, B, C, D, E, F, G, H are the 8 vertices.
AB, BC, CD, DA, EF, FG, GH, HE, AE, DH, BF, CG are the 12 edges.
ABCD, EFGH, ADHE, BCGF, ABFE and DCGH are the 6 faces
B. vertex
Vertex is the point where faces meets.
A is the vertex for AB, AD and EA.
C. Prism
A cuboid is also known as rectangular prism because a rectangular prism has six rectangular shaped sides with all sides at an angle 90° to each other.
Therefore, it can also be called a cuboid.
D. Tetrahedron
The tetrahedron is a polyhedron with a flat polygon base and the triangular faces that connect the base to a common point. Therefore, it is called a triangular pyramid.
Define Euler's relation between the number of faces, number of edges and number of vertices for various 3-dimensional figures.
Leonhard Euler has defined the relation between the number of faces, number of edges and number of vertices for various 3-dimensional figures is called as Euler's formula. This formula works with shapes called Polyhedron. A Polyhedron is a closed solid shape which has flat faces and straight edges like cube.
According to him
F + V – E = 2
Where F denotes the number of face
V denotes the number of vertices
E denotes the number of edges.
How many edges are there in a
A. cuboid
B. tetrahedron
C. triangular prism
D. square pyramid?
A. 12
A Cuboid has twelve edges.
AB, BC, CD, DA, EF, FG, GH, HE, AE, DH, BF, CG are the 12 edges.
B. 6
A Tetrahedron has six edges.
OA, OB, OC, AB, AC, BC are the 6 edges.
C. 9
A Triangular prism has nine edges.
AB, BC, CA, DE, EF, FD, AD, BE, CF are the edges.
D. 8
A Square Pyramid has eight edges.
AB, BC, CD, DA, OA, OB, DC, OD are the edges.
How many faces are there in a
A. cube
B. pentagonal prism
C. tetrahedron
D. pentagonal pyramid?
A. 6
A Cube has six faces.
ABCD, EFGH, ADHE, BCGF, ABFE and DCGH are the 6 faces
B. 7
A pentagonal prism has seven faces.
ABGF, AEJF, EDIJ, CDIH, BCGH, ABCDE and FGHIJ are the faces.
C. 4
A Tetrahedron has four faces
OAB, OAC, OBC and ABC are the faces.
D. 6
A pentagonal pyramid has six faces.
OAB, OBC, OCD, OAE, ODE and ABCDE are the faces.
How many vertices are there in a
A. cuboid
B. tetrahedron
C. pentagonal prism
D. square pyramid?
A. 8
A Cuboid has eight vertices.
A, B, C, D, E, F, G, H are the vertices.
B. 4
A Tetrahedron has four vertices.
O, A, B, C are 4 the vertices.
C. 10
A pentagonal prism has ten vertices.
A, B, C, D, E, F, G, H, I, J are the 10 vertices.
D. 5
A Square Pyramid has five vertices.
O, A, B, C, D are the vertices.
Verify Euler's relation for each of the following:
A. A cube
B. A tetrahedron
C. A triangular prism
D. A square pyramid
A.
According to Euler’s Formula
F + V –E = 2
Where F denotes the number of face
V denotes the number of vertices
E denotes the number of edges.
B.
According to Euler’s Formula
F + V –E = 2
Where F denotes the number of face
V denotes the number of vertices
E denotes the number of edges.
C.
According to Euler’s Formula
F + V –E = 2
Where F denotes the number of face
V denotes the number of vertices
E denotes the number of edges.
D.
According to Euler’s Formula
F + V –E = 2
Where F denotes the number of face
V denotes the number of vertices
E denotes the number of edges.