Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two dimensional objects

All the sides of a $5$ 5 cm cube are painted. How many $1$ cm cubes can be cut out from it? How many of these cubes will have no painted sides?

All the sides of a $5$ cm cube are painted. How many $1$ cm cubes can be cut out from it? How many of these cubes will have one painted sides?

All the sides of a $5$cm cube are painted. How many $1$ cm cubes can be cut out from it? How many of these cubes will have two painted sides?

All the sides of a 5 cm cube are painted. How many 1 cm cubes can be cut out from it? How many of these cubes will have three painted sides?

The figure $\left(X\right)$ given is folded to form a box. Choose the cubes that are similar to the cube formed:

Draw a cuboid with its dimension as seen from top, side and front views.

Is it possible to create a polyhedron with $8$ faces, $12$ vertices and $18$ edges? Justify.

To which of the given solids is Euler's formula applicable?

The total surface area of cube 'A' is $128 \mathrm{cm}²$ more than its curved surface area. If each edge of cube 'B' is $75\%$ more than that of cube 'A', then find the sum of the curved surface area and the total surface area of cube 'B'

How many edges, faces and vertices do the Square-based pyramid have?

What is the cube?

The length of the space diagonal of a cuboid with the length as $12 \mathrm{cm}$, breadth as $7 \mathrm{cm}$ and height as $5 \mathrm{cm}$, is

Find the length of the space diagonal of a cuboid with the length as $5 \mathrm{cm}$, breadth as $4 \mathrm{cm}$ and height as $3 \mathrm{cm}$.

A cuboid with the length as $5 \mathrm{cm}$, breadth as $4 \mathrm{cm}$ and height as $3 \mathrm{cm}$. The length of the face diagonal of the cuboid in the plane of breadth and height is $\sqrt{50} \mathrm{cm}$.

The number of face diagonals of a cuboid is 

Explain why this shape is not a prism.

This is a:

Name this shape and describe it using the words "faces", "edges", and "vertices".

This is the net for a:

This $3\mathrm{D}$ shape is a: