cube of side 4 cm is painted green on the pair of one opposite surface, red on the pair of another opposite surface and black on remaining pair of opposite surfaces. The cube is now divided into smaller cubes of equal size of 1 cm each.Find the number of smaller cubes with two surfaces painted.
Answers
Given:
Side of the cube = 4cm
Paint on one opposite side = Green
Paint on the other opposite side = Red
Size of smaller cubes = 1cm
To Find:
The number of smaller cubes with two surfaces painted.
Solution:
On dividing the cubes will be = 4 x 4 x 4
= 64
Now,
The corner cubes have three faces painted = 2 x 2 x 2 = 8
Thus, - 64 - 8
= 56
The middle cubes all have only one side painted.
Whereas,we have 4 of these for each cube face,
Thus, -
= 4 x 6
= 24
Now,
56 – 24
= 32
Answer: the number of smaller cubes with two surfaces painted is 32.
Number of smaller cubes with exactly two surfaces painted are 24 if cube of side 4 cm is painted and divided into smaller cubes of equal size of 1 cm each
Given:
- cube of side 4 cm
- painted green on the pair of one opposite surface
- red on the pair of another opposite surface
- black on remaining pair of opposite surfaces
- cube is divided into smaller cubes of equal size of 1 cm each.
To Find:
Number of smaller cubes with two surfaces painted.
Solution:
Cube cut in n x n x n
Exactly 3 faces painted = 8
Exactly 2 faces painted = 12 * (n - 2)
Exactly 1 face painted = 6 * (n - 2)(n-2)
No Face painted = (n - 2)³ = 64
cube of side 4 cm is divided into smaller cubes of equal size of 1 cm each.
Hence 4 x 4 x 4
Exactly 3 faces painted = 8
Exactly 2 faces painted = 12 * (4 - 2) = 24
Exactly 1 face painted = 6 * (4 - 2)(4-2) = 24
No Face painted = (4 - 2)³ = 8
Number of smaller cubes with exactly two surfaces painted are 24
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