English, asked by kagitasiva555, 11 months ago

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

Answered by bhagyashreechowdhury
9

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

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Answered by heyitsmejai
0

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

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