Answer:
5400 cubes can be fit into the prism.
Step-by-step explanation:
We are given the dimensions of prism as:
5 units by 5 units by 8 units i.e. 5 units×5 units×8 units.
Hence, the volume of the prism is given by:
Volume of prism=5×5×8=200 cubic units
Also the edge length of cube is given by= 1/3 unit.
Hence volume of 1 cube=
Hence volume of 1 cube= (1/27) cubic units.
Let 'n' cubes can be fitted into the prism.
Hence we have the relation as:
Volume of prism=n×Volume of 1 cube.
200=n×(1/27)
n=200×27
n=5400
Hence 5400 cubes can be fitted into the prism.
Answer: iii. (5 x 3) x (5 x 3) x (8 x 3)
Explanation:
If we ignored the smaller cubes, then the prism itself has the volume of 5 x 5 x 8 cubic units.
Now consider the smaller cubes. We can fit 3 to each unit (because 3*(1/3) = 1). This means each dimension is tripled.
We go from 5 x 5 x 8 to (5 x 3) x (5 x 3) x (8 x 3)
