Please help, I am unable to help my son with this problem and its due for school tomorrow. Thanks.

Question

Marsha constructed a large cube from 64 smaller cubes. Marsha then painted the outside of the large cube green. Later, when she took apart the large cube, Marsha noticed that some of the small cubes had paint on 3 faces, some had paint on 2 faces, some had paint on 1 face and some had no paint on them at all. How many of each kind of small painted cube (number of faces painted) were there?

Answer 1

Hi Cathy--

 

A cube's volume (in this case, the number of small cubes in the big cube) is determined by multiplying the length, times the width, times the height. And remember that in a cube, all three of those dimensions are going to be the same.

 

Since your volume is 64, you will pile up the 64 little cubes so that they form a larger cube whose length, width, and height are all 4 cubes across. (Because 4 x 4 x 4 is 64.)

 

The ones painted on three sides will be the ones at each of the big cube's 8 corners.

 

The ones painted on 2 sides will be the ones running along the edges of the big cube between the corner ones you already painted. (There should be 24 of those, I think!)

 

The ones painted on just 1 side will be the 4 in the middle of each of the 6 sides, so that's 24 of those.

 

And the ones not painted at all will be the 8 "inside the box" that you couldn't see or reach with the paintbrush.

 

If you can draw this or have some legos or blocks to build it with, it's WAY easier to visualize!

 

Hope this helps.

 

Matt in NY

Answer 2

The cube is 4 X 4 X 4.

Draw a picture.

 

The cubes with three faces painted are the cubes at the corners. There are 8 corners.

The cubes with two faces painted are the two cubes in each edge. There are 12 edges. There are 24 of these cubes.

The cubes with one face painted are the four cubes in the center of each side. There are six face. There are 24 of these cubes.

The cubes with no paint number 64 - 8 - 24 - 24 = 8.