a six centimeter cube is painted green on all sides .it is cut into two centimeters cubes.how many cubes will be there with two side painted
Answers
The dimension of the big cube is 6cm.
Its volume is :
6 × 6 × 6 = 216cm³
The volume of one cube to be cut from the larger cube is :
2 × 2 × 2 = 8 cm³
The number of cubes to be formed are :
216/8 = 27 cubes.
The cubes at the corners will have three faces painted.
The cube has 8 corners and each corner has one cube and hence we have 8 cubes with 3 sides painted.
To see this clearly, we need a diagram of a large cube divided into 27 smaller cubes.
In the image below we have the dotted cubes as the cubes with two sides painted, the striped ones are the ones with three sides painted and the plain ones are the ones with one side painted.
From the diagram we see that there are 12 cubes with two sides painted and 6 cubes with one side painted.
This adds up to 12 + 8 + 6 = 26
We therefore have only one cube with no side painted.
See the image below.