2) All sides of a cube having side 12 cm are painted, then small cubes having side 3 cm are cut, find the number of cubes having no colour on surface?
To find the number of small cubes that have no color on their surface, we can calculate the number of small cubes that have at least one face painted and subtract it from the total number of small cubes.
The total number of small cubes can be found by dividing the length of one side of the larger cube (12 cm) by the length of one side of the smaller cube (3 cm) and then cubing the result:
Total number of small cubes = (12 cm / 3 cm)^3 = 2^3 = 8
Now, let's calculate the number of small cubes that have at least one face painted. Each face of the larger cube has 4 small cubes attached to it, so there are 6 faces * 4 small cubes per face = 24 small cubes with at least one painted face.
Therefore, the number of small cubes with no color on their surface is:
Number of cubes with no color = Total number of small cubes - Number of cubes with at least one painted face
Number of cubes with no color = 8 - 24 = -16
However, it is not possible to have a negative number of cubes, so in this case, there are no small cubes that have no color on their surface.
I hope this helps! Let me know if you have any more questions.
Answers & Comments
Step-by-step explanation:
To find the number of small cubes that have no color on their surface, we can calculate the number of small cubes that have at least one face painted and subtract it from the total number of small cubes.
The total number of small cubes can be found by dividing the length of one side of the larger cube (12 cm) by the length of one side of the smaller cube (3 cm) and then cubing the result:
Total number of small cubes = (12 cm / 3 cm)^3 = 2^3 = 8
Now, let's calculate the number of small cubes that have at least one face painted. Each face of the larger cube has 4 small cubes attached to it, so there are 6 faces * 4 small cubes per face = 24 small cubes with at least one painted face.
Therefore, the number of small cubes with no color on their surface is:
Number of cubes with no color = Total number of small cubes - Number of cubes with at least one painted face
Number of cubes with no color = 8 - 24 = -16
However, it is not possible to have a negative number of cubes, so in this case, there are no small cubes that have no color on their surface.
I hope this helps! Let me know if you have any more questions.