How do I approach this problem? "A cube of 8cm x 8cm x 8cm is divided into..."

[Mac07]

How do I approach this problem? "A cube of 8cm x 8cm x 8cm is divided into..."

[FONT=&quot]A cube of 8cm x 8cm x 8cm is divided into smaller cubes of 1cm x 1cm x 1cm 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.[/FONT]
[FONT=&quot]Find the sum of the numbers on the cubes along the two body diagonals of the largest cube.

[/FONT][FONT=&quot]I'm not able to visualise what's given in the problem.[/FONT]

[FONT=&quot]I need a little push here.
Any help would be appreciated.[/FONT]

 

[Deleted member 4993]

A cube of 8cm x 8cm x 8cm is divided into smaller cubes of 1cm x 1cm x 1cm 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.
Find the sum of the numbers on the cubes along the two body diagonals of the largest cube.

I'm not able to visualize what's given in the problem.

I need a little push here.
Any help would be appreciated.

I cannot visualize it either.

The problem states that the smaller cubes are of equal volume (1cm x 1cm x 1cm).

Then it speaks of "the smallest volume " and " largest cube" and all such things .....

I believe, your instructor tried to make-up a "cute" problem and nomenclature got out of hand!!

 

[HallsofIvy]

[FONT=&quot]A cube of 8cm x 8cm x 8cm is divided into smaller cubes of 1cm x 1cm x 1cm 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.[/FONT]
[FONT=&quot]Find the sum of the numbers on the cubes along the two body diagonals of the largest cube.[/FONT]

?? A cube has four such diagonals!

[FONT=&quot]I'm not able to visualise what's given in the problem.[/FONT]

[FONT=&quot]I need a little push here.
Any help would be appreciated.[/FONT]

An 8 cm by 8 cm by 8 cm cube has volume 8^3= 512 cubic cm. Each small cube has volume 1 cubic cm so there are 512 "small cubes" forming the large cube. If you "extend the sides of the cube to the outer surface of the largest cube" (I think that should be simply "the large cube" since there are only two sides of the cube) you three rectangular solids each 1 cm by 1 cm by 8 cm so having volume 8 cubic cm. The total volume of all three is 24 cubic cm but that is counting the small cube itself 3 times- we need to subtract off 2. The volume formed is 22 cubic cm.

But that is the same for all of the cubes. If my interpretation is correct, you only need to find the length of the diagonals (and subtract three for the small cube where the four diagonals overlap) and multiply by 22.