What should the side lengths of each cubic block used to find the volume be?

Question

My math question that I have is:

Tristan’s fish tank is 1/2 yard long, 1/6 yard wide, and 1/3 yard high. (Note that the fish tank is in the shape of a rectangular prism and not a cube.) One way of finding the volume of the tank is by dividing the tank into cubic blocks.

What should the side lengths of each cubic block used to find the volume be?

I'm not sure what formula I would use to find out the side lengths of each cubic block would be? I can find out what the volume of the tank is, which is one of the other questions, but this question stumped me and I can't seem to find any answers online to help me figure it out.

Answer 1

Tristan’s fish tank is 1/2 yard long, 1/6 yard wide, and 1/3 yard high. (Note that the fish tank is in the shape of a rectangular prism and not a cube.) One way of finding the volume of the tank is by dividing the tank into cubic blocks.

What should the side lengths of each cubic block used to find the volume be?

The volume of the rectangular prism is:

(1/2 yd) * (1/6 yd) * (1/3 yd) = 1/36 yd³

You may make cubes that 'fit' the dimensions of the tank. A cube of (1/6 yd)*(1/6 yd)*(1/6 yd) would fit -- because 6 is the LCM of 2, 6, and 3. In terms of this cube, the tank is (3 cube sides)*(1 cube side)*(2 cube sides).

Now, this small cube is (1 in)*(1 in)*(1 in). [because 1 inch is 1/36 yard]

So, the fish tank can be filled using 1-inch cubes: 18x6x12.

That is 1296 cubic inches, which is 1/36th of a cubic yard [ 46,656 cubic inches]

The LCM of 2, 6, and 3 is the least common multiple:

Multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 39, 40, ...

Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ...

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, ...