Question

27 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
exactly one face
painted?​

Answer 1

Answer:

27 cubes are combined to form a larger cube.

The larger cube is painted on all 6 sides.

Let the side of one small cube be x cm.

Then obviously the area of one side of a small cube will be x²cm².

Area of the cube would be x³, area of 27 cubes would be 27×x³

Now,

Side of the bigger cube = ∛(Area of the bigger cube)

S₁=∛(27×x³)

S₁=3x cm.

Now, the side of small cube is x, side of bigger cube is 3x.

Now, the area of one side of the bigger cube = (S₁)²

= (3x)² = 9x².

Cubes in one side - the ratio of the area of the side of bigger cube and smaller cube.

Cubes in one side - 9x²÷x²:- 9.

Now we can picture this, with one big cube with 9 smaller cubes, see the file attached below, I used ms paint.

See the figure, the black coloured cubes have 2 or 3 sides painted, so for EACH SIDE only one cube is painted.

Thus, FOR 6 SIDES IT WILL BE 6×1 = 6.

ANSWER: 6 SIDES.

HOPE THIS HELPS :D