Group QuestionAnswer the following question based on the information given below.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 the numbers on the cubes along the two body diagonals of the largest cube.a)512b)200c)800d)400Correct answer is option 'D'. Can you explain this answer?

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Group Question

Answer the following question based on the information given below.

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 the numbers on the cubes along the two body diagonals of the largest cube.

a)
512
b)
200
c)
800
d)
400

Correct answer is option 'D'. Can you explain this answer?

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Group QuestionAnswer the following question based on the information g...

Consider perpendiculars from the inner most vertex of the smaller corner cube to the closest surfaces of the largest cube.
The perpendiculars and the surfaces of the largest cube will enclose a volume of 1 cm³.
The same is true for all the corner cubes. So, all the corner cubes are numbered 1.
Now consider the next cube along the body diagonal.
Smallest possible perpendiculars to the surfaces of the largest cube those enclose this smaller cube are of length 2 cm each.
So, the volume enclosed by the perpendiculars and the surfaces of the largest cube will be 8 cm³.
This cube is numbered 8.
Similarly, the numbers on the cube along the body diagonals will be perfect cubes of numbers starting from 1 to 4 and 4 to 1 on the other side.
The same pattern will be followed for both the body diagonals.
So the numbers on any body diagonal will be 1,8, 27, 64, 64, 27, 8 and 1
So, the required sum = 4 * (1 + 8 + 27 + 64) = 400
Hence, option 4.

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Group QuestionAnswer the following question based on the information given below.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 the numbers on the cubes along the two body diagonals of the largest cube.a)512b)200c)800d)400Correct answer is option 'D'. Can you explain this answer?

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