Representing 3-D in 2-D

(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.

(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.

(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.

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;

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.

The map showing the way my friend's home to the venue of my birthday party is shown below:

Map of the post office is shown below:

Map of the ground floor of my school is shown below:

Assertion (A) is false but Reason (R) is true.

Explanation

A rectangular pyramid has only one rectangular face, which is its base. The other 4 faces are triangular and meet at a common vertex (the apex). Thus, it has 5 faces in all, but they are not all rectangular.

So, Assertion (A) is false.

A pyramid is named according to the shape of its base, such as triangular pyramid, rectangular pyramid, or pentagonal pyramid.

So, Reason (R) is true.

Hence, option 4 is the correct option.

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Explanation

A cone is not a polyhedron because it has a curved surface.

So, Assertion (A) is true.

The definition of a polyhedron is a solid bounded by flat polygonal faces (like squares, triangles, or rectangles).

So, Reason (R) is true.

Hence, option 1 is the correct option.

To check which net cannot make a cube, imagine folding the squares along the edges.

• A valid cube net must fold into 6 different faces without overlapping.

Let's analyze each option:

Option A: This is a classic "1-3-1-1" style net. The faces fold perfectly around the central 3-square column, with the top-left and middle-right squares folding up to form the top and bottom lids.

Option B: This is the standard, most recognizable "Latin Cross" net (a 1-4-1 configuration). The central column of 4 forms the four sides, and the two wings fold up to form the remaining two opposite faces.

Option C: Both horizontal extensions are on the same side (the left) of the central vertical line. When folded, these squares will overlap each other, leaving the right side of the cube completely wide open.

Option D: This is a "3-3" zig-zag style net (often referred to as a step net). When folded, the faces shift perfectly into position without overlapping to form a complete cube.

(a), (b), and (d) all have balanced faces on opposite sides that fold cleanly without overlapping to cover all 6 sides of a cube.

Therefore, (c) cannot make a cube.

Hence, option 3 is the correct option.

From the given net, the pairs of opposite faces of the die are :

• □ lies opposite •
• $+ \text{ lies opposite } \circ$
• △ lies opposite ▬

Now, examining each option :

Option 1 : ○ is shown on the top and + is shown on a visible side. Since ○ and + lie on opposite faces, they cannot both be visible at the same time. So, option 1 is incorrect.

Option 2 : △ is shown on the top and ▬ is shown on a visible side. Since △ and ▬ lie on opposite faces, they cannot both be visible at the same time. So, option 2 is incorrect.

Option 4 : • is shown on the top and □ is shown on a visible side. Since • and □ lie on opposite faces, they cannot both be visible at the same time. So, option 4 is incorrect.

Option 3 : △ is shown on the top, • on the front, and ○ on the right side. None of these are pairs of opposite faces, and this arrangement is consistent with the way the given net folds into a cube.

Hence, option 3 is the correct option.

Let us examine each figure one by one.

• (P): This figure has 6 squares, but 5 of them are in one straight row. When folded, some faces overlap, so it cannot form a solid cube. Hence, (P) is not a net of a solid.
• (Q): This figure has 1 square and 4 triangles attached to it. When folded, the square becomes the base and the triangles form the side faces. So, it forms a square pyramid. Hence, (Q) is a net of a solid.
• (R): This figure has 2 hexagons and only 3 rectangles. To form a hexagonal prism, we need 2 hexagons and 6 rectangles. So, (R) is not a net of a solid.
• (S): This figure has 3 rectangles and 2 triangles. These fold to form a triangular prism. Hence, (S) is a net of a solid.
• (T): This figure has a sector of a circle and a circle. These fold to form a cone. Hence, (T) is a net of a solid.
• (U): This figure has 1 rectangle and 2 circles. These fold to form a cylinder. Hence, (U) is a net of a solid.

Therefore, only (Q), (S), (T) and (U) are nets of solids.

Hence, option 3 is the correct option.

The eraser is shaped like a 3D 5-pointed star prism (a star shape with thickness).

A 5-pointed star has 10 vertices along its outline — 5 outer points (the tips of the star) and 5 inner points (where adjacent star arms meet). So, each star-shaped face has 10 edges.

The 3D star prism has :

• 10 edges along the outline of the front star-shaped face
• 10 edges along the outline of the back star-shaped face
• 10 edges connecting the corresponding vertices of the front face to the back face

Total number of edges = 10 + 10 + 10 = 30.

Hence, option 3 is the correct option.