Answer:
135 Cubes
Step-by-step explanation:
Here we are given volume of a rectangular prism as 5 cubic units. And we are asked to find the number of cubes that can be inscribed in this whose side is
[tex]\frac{1}{3}[/tex]
Number of cubes that can be inscribed in the rectangular prism is the the ratio of the Volume of rectangular prism and the volume of the cube to be inscribed.
Volume of the cube to be inscribed = [tex](side)^{3}[/tex]
Side = [tex]\frac{1}{3}[/tex]
Volume = [tex](\frac{1}{3})^{3}[/tex]
= [tex]\frac{1}{27}[/tex]
Hence Total number of cubes which can be inscribed
= [tex]\frac{5}{ \frac{1}{27}}[/tex]
= [tex]\frac{5 \times 27}{1}[/tex]
= [tex]135[/tex]
The 135 cubes of sides [tex]\frac{1}{3}[/tex] units can be inscribed
