a pyramid of 1*1*1 of cubes is formed.
Bottom layer is 9*9 arrangment
then second layer is 7*7 arrangment then
third layer is 5*5 arrangment
4th layer 3*3 arrangment
5th layer is a single cube.
If the sides and tops are painted not the bottom. S how many square centimeters got painted
A suggestion as to how you might want to approach this problem......
First, if each cube is 1 * 1 * 1 (and I will assume the unit is cm, since the question asks how many square cm will be painted), then a FACE of such a cube will be 1 cm by 1 cm, or 1 cm^2. Count the painted faces, and that will be the number of square centimeters that get painted.
Start with the TOP layer.....that is just ONE cube. How many of its sides will be painted? How many square centimeters does that give you so far.
Then look at the next layer down (3 cubes by 3 cubes). One cube (the one directly under the cube in the top layer) won't be painted at all, will it? And how about the rest of the cubes in that layer. Do you see that some of them will be painted on three sides (why? how many of those will you have? How many square centimeters will this represent)? And SOME of them will be painted on just two sides....again, do you see why? And how many square centimeters will this add to your "painted total"?
Move down to the next layer (the one which is 5 X 5 squares, and continue in this manner....by this point, you may begin to see a pattern. If not, you can continue in exactly this way until you get to the bottom (9 X 9) layer.
I hope this helps you.
