State whether true (T) or false (F) :
(i) A cube has 8 edges.
(ii) A cuboid has more edges than vertices.
(iii) A cube has all edges equal.
(iv) A cone has only one face.
(v) A cylinder has only one vertex.
(vi) A cylinder has two flat faces.
Answer
(i) False
Reason — A cube has 12 edges, not 8. It has 8 vertices.
(ii) True
Reason — A cuboid has 12 edges and 8 vertices. Since 12 is greater than 8, this statement is correct.
(iii) True
Reason — By definition, a cube is a 3D shape in which every face is a square. Therefore, all 12 edges are equal in length.
(iv) False
Reason — A cone has two faces: one flat circular face (the base) and one curved surface.
(v) False
Reason — A cylinder has no vertices. It has two circular edges, but no sharp corners or points where edges meet.
(vi) True
Reason — A cylinder has two identical flat circular faces (the top and the bottom) and one curved surface connecting them.
Give two examples of each one of :
(i) a cuboid
(ii) a cube
(iii) a cylinder
(iv) a cone
Answer
(i) a cuboid
Examples: Brick, Matchbox.
(ii) a cube
Examples: Dice, Sugar cube.
(iii) a cylinder
Examples: Gas cylinder, Tubelight.
(iv) a cone
Examples: Ice-cream cone, Conical tent.
Fill in the blanks :
(i) A cuboid has ............... lateral faces.
(ii) The number of edges in a cube is ............... .
(iii) A cylinder has ............... faces. The number of flat faces is ............... and that of curved faces is ............... .
(iv) A cylinder has ............... edges.
(v) A cone has one ............... face and one ............... face.
(vi) A cuboid has six ............... faces.
Answer
(i) A cuboid has 4 lateral faces.
(ii) The number of edges in a cube is 12.
(iii) A cylinder has 3 faces. The number of flat faces is 2 and that of curved faces is 1.
(iv) A cylinder has 2 edges.
(v) A cone has one curved face and one flat face.
(vi) A cuboid has six rectangular faces.
Draw any four possible nets for a cube.
Answer
Any four possible nets of a cube are shown below:
Net 1:
When this net is folded to form a cube:
1 lies opposite 5; 2 lies opposite 4; 3 lies opposite 6;
Net 2:
When this net is folded to form a cube:
1 lies opposite 4; 2 lies opposite 6; 3 lies opposite 5;
Net 3:
When this net is folded to form a cube:
1 lies opposite 6; 2 lies opposite 4; 3 lies opposite 5;
Net 4:
When this net is folded to form a cube:
1 lies opposite 3; 2 lies opposite 5; 4 lies opposite 6;
Analyse the following nets of cubes and fill in the blanks :
When Net (X) is folded to form a cube :
(i) A lies opposite ...............
(ii) F lies opposite ...............
When Net (Y) is folded to form a cube :
(i) △ lies opposite ...............
(ii) □ lies opposite ...............
Answer
When Net (X) is folded to form a cube :
(i) A lies opposite C
(ii) F lies opposite E
When Net (Y) is folded to form a cube :
(i) △ lies opposite #
(ii) □ lies opposite -
Explanation
In Net (X) :
(i) A is separated from C by one square (B). So, A is opposite C.
(ii) Once the central column is folded, the wings E and F will fold up to face each other. So, F is opposite E.
In Net (Y) :
(i) △ is the wing on one side and # is at the bottom of the fold. When folded, the Triangle will face the #.
(ii) – is separated from the Square symbol by one square (O). So, – is opposite the Square symbol.