512 smaller but identical cubes have been put together to form a larger cube. This larger cube is now painted on all 6 faces. How many of the smaller cubes have at least one faces painted?
Answers
296 of the smaller cubes have at least one faces painted.
Explanation:
It is given that, 512 smaller but identical cubes are joined to form a large cube.
Volume of cube = side³
∴ Side of the larger cube will be, n = ∛512 = 8
Now,
The large cube is given to be painted on all 6 faces and in order to calculate the no. of smaller cubes that have at least 1 faces painted, we have find the cubes with one face painted, cubes with two face painted and cubes with three faces painted.
So,
1. Cubes with 1 face painted:
No. of smaller cubes with 1 face painted = 6 × (n-2)² = 6 × (8-2)² = 6 × 36 = 216
2. Cubes with 2 faces painted:
No. of smaller cubes with two faces painted = 12 × (n - 2) = 12 × (8 - 2) = 12 × 6 = 72
3. Cubes with 3 faces painted:
We know that each cube has 8 corners and only the corners of the cube can have three of their faces painted.
So, no. of smaller cubes having exactly three faces painted = 8
Thus,
The no. of smaller cubes having at least one faces painted is,
= 216 + 72 + 8
= 296
--------------------------------------------------------------------------------------
Also View:
216 smaller but identical cubes have been put together to form a larger cube. This larger cube is now painted on all 6 faces. How many of the smaller cubes have at least three faces painted?
https://brainly.in/question/10656777
125 small but identical cubes are put together to form a large cube. this large cube is now painted on all six faces. how many of the smaller cubes have no face painted at all. select one: a. 27 b. 64 c. 36 d. 8
https://brainly.in/question/5497186
Answer:
512 smaller but identical cubes have been put together to form a larger cube. This larger cube is now painted on all 6 faces. How many of the smaller cubes have no face painted at all?
Select one:
a. 218
b. 216
c. 212
d. 296
Explanation:
512 smaller but identical cubes have been put together to form a larger cube. This larger cube is now painted on all 6 faces. How many of the smaller cubes have no face painted at all?
Select one:
a. 218
b. 216
c. 212
d. 296