A 6inch cube is painted on the outside and cut into 27 smaller cubes. What is the total of the areas of the unpainted surfaces?

Question

PLEASE help!!! For an answer, I got 432 but i’m not sure if i did it correctly.

Answer 1

The way I would approach this problem is to 1) determine the surface area painted, 2) Determine what the surface area of the 27 individual cubes would be and finally 3) subtract the surface area of the 27 cubes by the surface area painted to get the total surface area of the UN-PAINTED.

So, the surface area painted for a 6 inch cube is 6 x 6 =36 inch^2 for ONE side, then multiply by 6 for the 6 faces of the cube for a total of 216 inch^2.

Next, you have to determine what the surface area of 27 individual cubes would be. The way I solved for this is to determine the volume of the larger cube, which is 6x6x6=216 inch^3. Now, by dividing this larger volume by 27 will give the volume of one of the 27 individual cubes, which is 8 inch^3. since volume of a cube is a cubed root, the cube root of 8 is 2. So the dimension of the smaller cube is 2 inches.

Now, since we now know the dimensions of the smaller cube, determine its surface area. 2 x 2=4 inch^2 x 6 for the 6 faces of the cube which is 24 inch^2 x 27 since there are 27 cubes. This TOTAL surface area is 648 inch^2.

Finally, subtract the total SA of the 27 cubes by the SA painted to get the remaining UN-PAINTED surface area. 648-216=432 inch^2.