A cube of 7cm 7cm 7cm is kept in the corner of a room and painted in three different colours, each face in one colour. The cube is cut into 343 smaller but identical cubes. How many smaller cubes do not have any face painted?
Answers
answer = 196
Step-by-step explanation:
volume of big cube = 343
no. of small cubes = 343
volume of small cubes = 1
area of big cube painted = 7×7×3 = 147
no.of smaller cubes do not have any face painted = 343-147 = 196
The number of smaller cubes does not have any face painted is 131.
Given:
A cube of 7cm, 7cm, and 7cm is kept in the corner of a room and painted in three different colors, each face in one color.
The cube is cut into 343 smaller but identical cubes.
To Find:
The number of smaller cubes does not have any face painted.
Solution:
To find the number of smaller cubes does not have any face painted, the number of cubes painted on three sides, two sides, and one side will be subtracted from the total cubes.
If a cube is cut into 343 smaller cubes then each cube will have sides of 7cm.
The number of cubes painted on three sides is present at the vertices of the larger cube. There are 8 such cubes.
The number of cubes painted on two sides is present at the edges of the larger cube. There are 54 such cubes.
The number of cubes painted on one side is present at the face of the larger cube. There are 150 such cubes.
The number of smaller cubes does not have any faces painted are
Thus, the number of smaller cubes does not have any face painted is 131.
#SPJ3