Question

Tristan's fish tank is yard long, yard wide, and 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?

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?

Answer:

the side lengths are 3 sides, 1 side and 2 sides  of each cubic block.

Step-by-step explanation:

The volume of the rectangular prism is:

$(1/2 \ yard) * (1/6 \ yard) * (1/3 \ yard) = 1/36 \ yard^3$

However: let's find their lowest common multiples to determine their side length.

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

Multiples of 6:   6, 12, 18, 24, 30, ...

Multiples of 3:   3, 6, 9, 12, 15, 18, 21, 24, 27, 30,  ...

The lowest common multiple for 2 , 6 and 3 is 6 .

Then in terms of the side length of each cubic block; we have :

1/2 × 6 = 3

1/6 × 6 = 1

1/3 × 6 = 2

So the side lengths are 3 sides, 1 side and 2 sides  of each cubic block