Answer:
48
Step-by-step explanation:
To find how many 1/3 cm length cubes fill the prism, we first need to find the volume, which is equal to
length * width * height = 1 cm * (2 + 2/3) cm * (2/3) cm
= 1 cm * (6/3 + 2/3) cm * (2/3) cm
= 1 cm * (8/3) cm * (2/3) cm
= (8/3) cm ² * (2/3) cm
= (16/9) cm³
Therefore, the volume is 16/9 cm³.
Next, one cube with side lengths of 1/3 has a volume of ((1/3) cm)³ = (1/27)³
We thus need to find how many of 1/27 goes into 16/9
If we multiply 16/9 by 1=3/3 (as 9*3=27), we can equalize the bases, making 16/9 = 48/27
All that's left is to figure out how many times 1/27 goes into 48/27, which is equal to (48/27)/(1/27) = 48
