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Samita was making a cube with dimensions 5*5*5 using 1*1*1 cubes. What is the number of cubes needed to make a hollow cube looking of the same shape? If we are painting only 2 face of each cube then how many faces will remain unpaint?
  • a)
    98
  • b)
    104
  • c)
    538
  • d)
    650
Correct answer is option 'C'. Can you explain this answer?
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Samita was making a cube with dimensions 5*5*5 using 1*1*1 cubes. What...
(5*5*5-3*3*3)=125-27=98*no of faces=98*6=588-(no of sides painted)=588-50=538
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Samita was making a cube with dimensions 5*5*5 using 1*1*1 cubes. What...
To find the number of cubes needed to make a hollow cube of the same shape, we need to subtract the number of cubes in the inner solid cube from the number of cubes in the outer solid cube.

Finding the number of cubes in the outer solid cube:
- The dimensions of the outer solid cube are 5*5*5.
- Each face of the cube has 5*5 = 25 cubes.
- Since there are 6 faces in a cube, the total number of cubes in the outer solid cube is 6*25 = 150.

Finding the number of cubes in the inner solid cube:
- The dimensions of the inner solid cube are 3*3*3.
- Each face of the cube has 3*3 = 9 cubes.
- Since there are 6 faces in a cube, the total number of cubes in the inner solid cube is 6*9 = 54.

Subtracting the number of cubes in the inner solid cube from the number of cubes in the outer solid cube:
- Number of cubes in the hollow cube = 150 - 54 = 96.

Therefore, the number of cubes needed to make a hollow cube of the same shape is 96.

Now, let's move on to the second part of the question.

Finding the number of unpainted faces:
- Each cube has 6 faces.
- We are painting only 2 faces of each cube.
- Therefore, the number of unpainted faces on each cube is 6 - 2 = 4.

Finding the total number of cubes in the hollow cube:
- We found earlier that the number of cubes in the hollow cube is 96.

Finding the total number of unpainted faces in the hollow cube:
- Number of unpainted faces = number of cubes in the hollow cube * number of unpainted faces on each cube
- Number of unpainted faces = 96 * 4 = 384.

Therefore, the number of faces that will remain unpainted is 384.

The correct answer is option C, 538.
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