How many .5 cm x.5 cm x .5 cm cubes are needed to completely fill a rectangular prism measuring 4 cm x 3 cm x 3 cm?
The linear dimensions have increased by factors of 8,6,6
So, the volume has increased by a factor of 8*6*6 = 288
288
To find out how many cubes are needed to completely fill the rectangular prism, you need to calculate the volume of the rectangular prism and then divide it by the volume of one cube.
The formula for calculating the volume of a rectangular prism is:
Volume = length x width x height
For the given rectangular prism with dimensions 4 cm x 3 cm x 3 cm, the volume is:
Volume = 4 cm x 3 cm x 3 cm = 36 cm³
Now, let's calculate the volume of one cube with dimensions 0.5 cm x 0.5 cm x 0.5 cm:
Volume of one cube = 0.5 cm x 0.5 cm x 0.5 cm = 0.125 cm³
To determine how many cubes are needed to fill the rectangular prism, divide the volume of the rectangular prism by the volume of one cube:
Number of cubes = Volume of rectangular prism / Volume of one cube
Number of cubes = 36 cm³ / 0.125 cm³ ≈ 288
Therefore, you would need approximately 288 cubes measuring 0.5 cm x 0.5 cm x 0.5 cm to completely fill the rectangular prism measuring 4 cm x 3 cm x 3 cm.