Question

For a project, Shalmali makes a dice having edge of length 30
m using cardboard. She draws small squares of side 7 cm on
die's 6 faces to show a different number from 1 to 6. Theses small
squares are coloured using black paint and remaining part of the
faces is coloured pink. Find the area coloured in pink colour. ????????

Answer 1

Answer:

First we will find the total number of ways by which 6 different colors can paint a cube. This turns out to be 6! (i.e. you have 6 choices for 1st face, 5 choices for 2nd, 4 choices for 3rd and so on). But this cannot be our final answer as this particular solution will Demands from us that we be able to distinguish between 6 identical sides of a cube when it is rotated. THIS is not possible.

Now what we need to do is to Fix cube so that repetition is prevented and the concern regarding identifying the sides becomes irrelevant. For this consider the Cube to be placed in a 3D space.

Consider: Each of the 4 sides being North, South, West, East respectively and the remaining 2 sides being Up and Down.

We can fix the Down side in 6 ways. This will automatically fix the Up side that is opposite to the Down. Among the remaining 4 sides fixing 1 will fix the rest. By fixing North side we fix South as well as East and West side, I.e. When North is fixed - South gets fixed.This results in the only way in which the four directions can be oriented. Hence numbers of ways of fixing North is 4 ways.

Now we have a total number of ways of painting - 6! AND Number of fixed positions for a cube - 6*4 = 24

Therefore total ways of painting a cube in given question -

-6! / (6*4) = 30

Answer 2

Answer:

• Total Surface Area of the dice= 6×(30)^2 cm^2=5400cm^2.
• Total Surface Area of the black paint= 6×(7)^2 cm^2 =294cm^2.
• Total black paint= 5400/294=18.36~18(approx.)
• Area of the pink paint ={5400-(294×18)}=5400-5292=108cm^2.

Therefore, area of the pink paint is 108cm^2.