8320 cubes can fit into the prism.
Solution:
Convert mixed fraction into improper fraction.
Length of the prism = 20 in
Width of the prism = 2 in
Height of the prism = [tex]3\frac{1}{4}=\frac{13}{4}[/tex] in
Volume of the prism = length × width × height
[tex]$=20\times2\times\frac{13}{4}[/tex]
= 130 in³
Volume of the prism = 130 in³
Length of the cube = [tex]\frac{1}{4}[/tex] in
Volume of the cube = length × length × length
[tex]$=\frac{1}{4} \times\frac{1}{4} \times\frac{1}{4}[/tex]
[tex]$=\frac{1}{64} \ \text{in}^3[/tex]
Volume of the cube = 0.015625 in³
[tex]$\text{Number of cubes}=\frac{\text{Volume of the prism}}{\text{Volume of cube}}[/tex]
[tex]$=\frac{130}{0.015625}[/tex]
= 8320
Number of cubes = 8320
Hence 8320 cubes can fit into the prism.
