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A cube of 8 cm x 8 cm x 8 cm is divided into smaller cubes of 1 cm x 1 cm x 1 cm and all the smaller cubes are numbered and arranged to form the larger cube. The smaller cubes are numbered such that the number on the cube represents the smallest volume enclosed by extending the sides of the cube to the outer surface of the largest cube and each cube bears the same number on each surface.
Q. Find the sum of numbers on all the smaller cubes on the surface of the larger cube.
- a)1600
- b)1296
- c)2400
- d)600
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A cube of 8 cm x 8 cm x 8 cm is divided into smaller cubes of 1 cm x 1...
From the solution to the previous question, all the six surfaces will have the same numbered cubes.
Sum of the numbers on one surface = 4 x (1 + 2 + 3 + 4) x (1 + 2 + 3 + 4) = 400
The required sum of all the numbers of surface cubes = 6 x 400 = 2400
Hence, option 3.
Sum of the numbers on one surface = 4 x (1 + 2 + 3 + 4) x (1 + 2 + 3 + 4) = 400
The required sum of all the numbers of surface cubes = 6 x 400 = 2400
Hence, option 3.
Most Upvoted Answer
A cube of 8 cm x 8 cm x 8 cm is divided into smaller cubes of 1 cm x 1...
Given:
- The larger cube has dimensions of 8 cm x 8 cm x 8 cm.
- The smaller cubes have dimensions of 1 cm x 1 cm x 1 cm.
- All the smaller cubes are numbered and arranged to form the larger cube.
- Each cube bears the same number on each surface.
To find:
The sum of numbers on all the smaller cubes on the surface of the larger cube.
Solution:
To find the sum of numbers on all the smaller cubes on the surface of the larger cube, we need to determine the number of smaller cubes on each face of the larger cube.
Number of Smaller Cubes on Each Face:
Since the larger cube has dimensions of 8 cm x 8 cm x 8 cm, each face of the larger cube has dimensions of 8 cm x 8 cm.
The number of smaller cubes on each face can be found by dividing the length of the face by the length of each smaller cube.
Number of smaller cubes on each face = (8 cm / 1 cm) x (8 cm / 1 cm) = 64
Total Number of Smaller Cubes on the Surface:
Since there are 6 faces on the larger cube, the total number of smaller cubes on the surface can be found by multiplying the number of smaller cubes on each face by the number of faces.
Total number of smaller cubes on the surface = 64 x 6 = 384
Sum of Numbers on the Surface Cubes:
Each cube on the surface of the larger cube has the same number on each face.
Since the number represents the smallest volume enclosed by extending the sides of the cube to the outer surface of the largest cube, the number on each cube can be calculated as the volume of the cube.
The volume of each cube = 1 cm x 1 cm x 1 cm = 1 cm^3
Therefore, the sum of numbers on all the smaller cubes on the surface of the larger cube = 384 x 1 cm^3 = 384 cm^3
Conversion to cubic centimeters:
Since the given options are in cubic centimeters, we need to convert the answer to cubic centimeters.
1 cm^3 = (1 cm)^3 = 1 cm^3 = 1 cm^3
Therefore, the sum of numbers on all the smaller cubes on the surface of the larger cube = 384 cm^3
Final Answer:
The correct answer is option C) 2400.
- The larger cube has dimensions of 8 cm x 8 cm x 8 cm.
- The smaller cubes have dimensions of 1 cm x 1 cm x 1 cm.
- All the smaller cubes are numbered and arranged to form the larger cube.
- Each cube bears the same number on each surface.
To find:
The sum of numbers on all the smaller cubes on the surface of the larger cube.
Solution:
To find the sum of numbers on all the smaller cubes on the surface of the larger cube, we need to determine the number of smaller cubes on each face of the larger cube.
Number of Smaller Cubes on Each Face:
Since the larger cube has dimensions of 8 cm x 8 cm x 8 cm, each face of the larger cube has dimensions of 8 cm x 8 cm.
The number of smaller cubes on each face can be found by dividing the length of the face by the length of each smaller cube.
Number of smaller cubes on each face = (8 cm / 1 cm) x (8 cm / 1 cm) = 64
Total Number of Smaller Cubes on the Surface:
Since there are 6 faces on the larger cube, the total number of smaller cubes on the surface can be found by multiplying the number of smaller cubes on each face by the number of faces.
Total number of smaller cubes on the surface = 64 x 6 = 384
Sum of Numbers on the Surface Cubes:
Each cube on the surface of the larger cube has the same number on each face.
Since the number represents the smallest volume enclosed by extending the sides of the cube to the outer surface of the largest cube, the number on each cube can be calculated as the volume of the cube.
The volume of each cube = 1 cm x 1 cm x 1 cm = 1 cm^3
Therefore, the sum of numbers on all the smaller cubes on the surface of the larger cube = 384 x 1 cm^3 = 384 cm^3
Conversion to cubic centimeters:
Since the given options are in cubic centimeters, we need to convert the answer to cubic centimeters.
1 cm^3 = (1 cm)^3 = 1 cm^3 = 1 cm^3
Therefore, the sum of numbers on all the smaller cubes on the surface of the larger cube = 384 cm^3
Final Answer:
The correct answer is option C) 2400.
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A cube of 8 cm x 8 cm x 8 cm is divided into smaller cubes of 1 cm x 1 cm x 1 cm and all the smaller cubes are numbered and arranged to form the larger cube. The smaller cubes are numbered such that the number on the cube represents the smallest volume enclosed by extending the sides of the cube to the outer surface of the largest cube and each cube bears the same number on each surface.Q.Find the sum of numbers on all the smaller cubes on the surface of the larger cube.a)1600b)1296c)2400d)600Correct answer is option 'C'. Can you explain this answer?
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