Question

All the faces of cubes are painted with green color.The cubes is cut into 64 equal small cubes. How many
small cubes have no faces colored ?
Select one:
O a. 16
O b. 24
O c. O
d. 8​

Answer 1

Step-by-step explanation:

Let this be the original cube .

It is cut into 64 small cubes ( demarcated by lines ) .

Let's go layer wise ( top to bottom )

There are 4 layers .

1st layer :-

All the cubes are painted .

No. Of unpainted cubes = 0

2nd layer :-

Only side cubes are painted , internal 4 cubes ( middle most ) are not painted .

No. Of unpainted cubes = 4

3rd layer:-

Same as layer 2

No. Of unpainted cubes= 4

4th layer:-

Same as layer 1 .

No unpainted cubes.

Total unpainted cubes= 8

Hope this answer helps .

Answer 2

Given :- All the faces of cubes are painted with green color. The cubes is cut into 64 equal small cubes.

To Find :- How many small cubes have no faces colored ?

A) 16

B) 24

C) 0

D) 8

Formula used :-

• Number of small cubes with 0 side painted= (n - 2)³ where n is side of bigger cube .
• Volume of cube = (side)³

Solution :-

Let us assume that, sides of bigger cube was x units .

So,

→ Volume of bigger cube = (side)³ = (x)³ = x³ units³

now, let us say 64 small cubes are formed with each side as 1 unit .

then,

→ x³ = 64

→ x³ = 4³

cube root both sides

→ x = 4 .

now,

→ Total number of small cubes with No faces colored = (n - 2)³ = (4 - 2)³ = (2)³ = 2 × 2 × 2 = 8 cubes (D) (Ans.)

Extra knowledge :-

• Number of small cubes with 1 sides painted = 6(n - 2)² = 6(4 - 2)² = 6 × (2)² = 6 × 4 = 24 cubes
• Number of small cubes with 2 sides painted = 12(n - 2) = 12(4 - 2) = 12 × 2 = 24 cubes
• Number of small cubes with 3 sides painted = 8 cubes .

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