From Alex
Grade 6 (middle)
Student

How do you find the volume cubic matter of a cube or space, example how many cubic feet in an example 6" high 4' X 6' rectangle

Thank You

Hi Alex
First you need all the dimensions in the same units, so if the units are inches your box is 6" high on a 48"x72" rectangle. Think about trying to fill this box with small cubes that are 1" by 1" by 1". These small cubes, called one inch cubes, each have a volume of 1 cubic inch.
   To fill your box with one inch cubes first cover the bottom. This takes 48 rows of small cubes, each row containing 72 cubes. Thus to cover the bottom takes 48 x 72 = 3456 cubes. Since your box is 6" high you need 6 layers of 3456 cubes or 6 x 3456 = 20736 cubes to fill the box. Since each cube has a volume of 1 cubic inch the box has a volume of 20736 cubic inches.
   What we did is put all three dimensions in the same units and then multiply the length times the width times the height. If you had choosen the units to be feet then the box is (1/2)' by 4' x 6' so the volume is (1/2) x 4 x 6 = 12 cubic feet.

Cheers
Penny