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Explanation: 1 Mark each
(i) A prism becomes a cylinder whenthe number of sides increases.
(ii) Whenthe number of sides of the pyramid increases, itbecomes a cone.

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Each part: 2 Marks
(a) There are 3 vertical columns of sugar bags in this box.
The first column has 9 bags of which 5 can be seen and the other 4 are completely hidden.
The second column has 6 bags of which 4 can be seen, and similarly, the third column has 3 bags.
So, the total number of bags = 9 + 6 + 3 = 18.
(b) Now, in the second column, we can see that there is space for 3 more bags and the third column has space for 6 more bags.
The remaining space can be filled with 2 more vertical columns, each having 9 bags.
So, there is a space in the box for $3+6+(9\times 2)=9+18=27$ more bags.

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Solution: 1 Mark each
A polyhedron is a solid with flat polygonal faces, straight edges and vertices.
(i) This is not true. The minimum number of faces a polyhedron can have is 4. Hence 3 triangles cannot be the faces of a polyhedron.
(ii) This is true. Apolyhedron with 4 triangles as faces is known as a regular tetrahedron.
(iii) This is true. Apolyhedron with 1 square and 4 triangular faces is known as a square pyramid.

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Definition: 2 Marks
Example: 1 Mark
A shape that has only two dimensions (such as width and height) and no thicknessis known as 2-D shape.In 2-D shapes, the sides are made of straight and curved lines.
Example: squares, circles, triangles
A 3-D shape is a solid which enclosesvolume and has length, breadth and height.3-D shapes have four properties that set them apart from 2-D shapes: faces, vertices, edgesand volume.
Example: sphere, cylinder, cube

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Each part: 2 Marks
(a) Sphere, cone and cylinder are not polyhedrons.
Sphere: Sphere has only one curved face and no polygons as faces. So it is not apolyhedron.
Cone: Cone has one circular face and the remaining part is a curved surface. So it is not apolyhedron.
Cylinder:Cylinderhas two circular faces and the remaining part is a curved surface. So it is not apolyhedron.
(b) (i) - (b)
(ii) - (a)
(iii) - (e)
(iv) - (c)
(v) - (d)

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Explanation: 1 Mark each
Acylindercan be thought of as a circular prism that is a prism with a circle as its base.
Aconecan be thought of a circular pyramid that is a pyramid with a circle as its base.

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Explanation: 2 Marks
A square prism has a square as its base. However, its height is not necessarily same as the side of the square.
Thus, a square prism can also be a cuboid.
All cubes are square prism but all square prisms need not be cubes.

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Each correct match: 1 Mark

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We need a square with same side length as that of the triangle. The resultant solid is known as a square pyramid.

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Each part: 1 Mark
From visual estimation, each column contains 4 boxes.

(a) 6 columns can be fit in the shelf.
In the 5th column, there is space for 2 more boxes.
and in the 6th column, there is space for 4 boxes.
$\therefore$ Number of boxes on the full shelf = 18 + 2 + 4 = 24 boxes
(b) If the length of the shelf is doubled, the shelf can have 12 columns.
If the height of the shelf is doubled, then each column can have 8 boxes.
$\therefore$ Total number of boxes on the full new shelf:
= $12\times 8$
= 96 boxes
(c)If the length of the shelf is halved, the shelf can have 3 columns.
If the height of the shelf is doubled, then each column can have 8 boxes
$\therefore$ Total number of boxes on the full new shelf:
= $3\times 8$
= 24 boxes
(d) If the length of the shelf is doubled, the shelf can have 12 columns.
If the height of the shelf is doubled, then each column can have 4 boxes.
$\therefore$ Total number of boxes on the full new shelf:
= $12\times 4$
= 48 boxes