Answer:
324 cubes.
Step-by-step explanation:
Let n be the number of cubes with edge length 1/12 meter.
We have been given the lengths of edges of a right rectangular prism as [tex]\frac{1}{2}[/tex] meter, [tex]\frac{1}{2}[/tex] meter and [tex]\frac{3}{4}[/tex] meter.
[tex]\text{Volume of rectangular prism}=L*B*H[/tex], where,
L = Length of prism,
B = Breadth of prism,
H = Height of prism.
[tex]\text{Volume of cube}=a^3[/tex], where a= length of each edge of the cube.
The volume of n cubes with each edge 1/12 will be equal to the volume of rectangular prism.
[tex]\text{Volume of n cubes}=\text{Volume of rectangular prism}[/tex]
[tex]n\times a^3=L*B*H[/tex]
Upon substituting our given values we will get,
[tex]n\times(\frac{1}{12})^3=\frac{1}{2}\times \frac{1}{2}\times \frac{3}{4}[/tex]
[tex]n\times\frac{1^3}{12^3}=\frac{1*1*3}{2*2*4}[/tex]
[tex]n\times\frac{1}{1728}=\frac{3}{16}[/tex]
Let us multiply both sides of our equation by 1728.
[tex]\frac{n}{1728}*1728=\frac{3}{16}*1728[/tex]
[tex]n=\frac{3}{16}*1728[/tex]
[tex]n=3*108[/tex]
[tex]n=324[/tex]
Therefore, 324 unit cubes can fit inside the given right rectangular prism.
