Question

A cube of side 16 cm, painted red and cut it into 4 cm small pieces of cube then answer the followings :
9. Find total number small cubes ?
(A) 64 (B) 32 (C) 48 (D) 84
10. How many small cubes are there which are having only three side painted ?
(A) 16 (B) 8 (C) 24 (D) 4


Pls explain

Answer 1

No of smaller cubes is 64 because 4x4x4
No of small cubes which are having only three side painted are 8 
because of 8 vertices

Answer 2

The total number small cubes is 64 and option(A) is correct.

The numbers of small cubes are there which are having only three side painted is 8 and option (B) is correct.

Step-by-step explanation:

Given:

A cube of side 16 cm, painted red and cut it into 4 cm small pieces of cube.

To Find:

The total number small cubes.

The numbers of small cubes are there which are having only three side painted.

Solution:

As given,a cube of side 16 cm, painted red and cut it into 4 cm small pieces of cube.

The total number small cubes $=\frac{Volume\ of\ cube\ of\ side\ 16 cm}{Volume\ of\ small \ cube\ of\ side\ 4cm }$

                                                  $=\frac{16^{3} }{4^{3} } =\frac{4096}{64} =64$

Thus,the total number small cubes 64 option(A) is correct.

In each side of the big cube, the smaller cubes at the edges will have more than one face painted.

The cubes which are situated at the corners of the big cube, have three faces painted.

Therefore, the number of small cubes at the corners of the big cube=8.

Thus,the numbers of small cubes are there which are having only three side painted is 8 and option (B) is correct.

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