**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.