How many .5 cm x.5 cm x .5 cm cubes are needed to completely fill a rectangular prism measuring 4 cm x 4 cm x 4 cm?
the linear dimension has increased by a factor of 8
so, volume has increased by a factor of 8^3 = 512
To find out how many .5 cm x .5 cm x .5 cm cubes are needed to completely fill a rectangular prism measuring 4 cm x 4 cm x 4 cm, you need to calculate the volume of the rectangular prism and then divide it by the volume of one cube.
First, calculate the volume of the rectangular prism:
Volume = Length x Width x Height
Volume = 4 cm x 4 cm x 4 cm
Volume = 64 cubic cm
Next, calculate the volume of one cube:
Volume = Length x Width x Height
Volume = 0.5 cm x 0.5 cm x 0.5 cm
Volume = 0.125 cubic cm
Finally, divide the volume of the rectangular prism by the volume of one cube to find out how many cubes are needed:
Number of cubes = Volume of rectangular prism / Volume of one cube
Number of cubes = 64 cubic cm / 0.125 cubic cm
Number of cubes = 512
Therefore, you would need 512 .5 cm x .5 cm x .5 cm cubes to completely fill the rectangular prism.