Question

Question 6:

Directions: One hundred and twenty-five cubes of the same size are arranged in the form of a cube on a table. Then a column of five cubes is removed from each of the four corners. All the exposed faces of the rest of the solid (except the face touching the table) are colored red. Now, answer these questions based on the above statement:

How many small cubes are there in the solid after the removal of the columns?How many cubes do not have any colored face?How many cubes have only one red face each?How many cubes have two colored faces each?How many cubes have more than 3 colored faces each?​

Answer 1

Step-by-step explanation:

Thank you for asking this question. Here is your answer:

There are 9 cubes named as m, n, o, p, q, r, s, t and u in layer 1,

And 4 cubes (in columns b, e, h and k) in each of the layers 2, 3, 4 and 5 got  one red face.

So there are 9 + (4 x 4) = 25 cubes

The final answer for this question is 25 cubes.

Answer 2

1. Since out of 125 total number of cubes, we removed 4 columns of 5 cubes each, the remaining number of cubes = 125 – (4 x 5) = 125 – 20 = 105.

2. Cubes with no paintings lie in the middle. So cubes which are below the cubes named as s, t, u, p, q, r, m, n, o got no painting. Since there are 4 rows below the top layer, total cubes with no painting are (9 x 4) = 36.

3. There are 9 cubes named as m, n, o, p, q, r, s, t and u in layer 1, and 4 cubes (in columns b, e, h, and k) in each of the layers 2, 3, 4 and 5 got one red face. Thus, there are 9 + (4 x 4) = 25 cubes.

4. The columns (a, c, d, f, g, i, j, l) each got 4 cubes in the layers 2, 3, 4, 5. Also in layer 1, h, k, b, e cubes got 2 faces colored. so total cubes are 32 + 4 = 36.

5. There is no cube in the block having more than three colored faces. There are 8 cubes (in the columns a, c, d, f, g, i, j and l) in layer 1 which have 3 colored faces. Thus, there are 8 such cubes.