CUBE AND DICE
CUBE
Cube is a 3D figure consisting of 6 square surface. A cube has $\\$ $\qquad$
If a cube is painted on all its surface with color and the cube is divided into various smaller cubes , then$\\$ $\qquad\qquad$
$\\$1. Eight Corner small cubes will be painted on its 3 sides. $\\$ 2. Between the corners and on edges the smaller cubes will be painted on 2 of its surface. $\\$ 3. Between all edges the cubes on outer surface will be painted on 1 side.$\\$ 4. Inside the cube some small cubes will not have paint on any of its surface.
let a cube of edge length n units is painted on all is surface and is divided into small cubes of edge lengths 1 unit each . $\\$ Tolal number of small such cubes obtained will be=${(n)}^{3}$ $\\$ Total number of small cubes with 3 sides painted = 8 $\qquad$ ( i.e Cubes at 8 corners ). $\\$ Total number of small cubes painted on two sides =12.(n-2) $\qquad $( On each edge there are (n-2) such cubes and total number of edges are 12 ). $\\$ Total number of small cubes painted on 1 side only = 6.${(n\,-\,2)}^{2}$ $\qquad$ ( There are ${(n\,-\,2)}^{2} $ number of cubes on each surface which are painted on one side only and there are 6 such faces ) $\\$ Total number of small cubes that are not painted on any of its surface = ${(n\,-\,2)}^{3} $ $\qquad$ ( The cubes which are inside and did not have any edge on surface of big cube ).
DICE
In the questions on dice two or three different positions of dice are shown, and in every position 3 surface on which number are written are given and question is what will be the number opposite of a number. $\\$ $\qquad \qquad $
The approach to solve such questions are every Dice or cube has 6 surface and every surface has four adjacent sides and only one side opposite to it.