We have to calculate the volume of this prism by the method given.
Each little cube have sides of 1/2 of an inch (lets call x to the length to the side of the little cube).
We then will count the multiple of the little cube side the prism has in each dimension.
The prism is 3 sides tall (3x), 5 sides wide (5x) and 7 sides deep (7x).
The volume of the prism is the product of this 3 dimensions, so we can express it as:
[tex]\begin{gathered} V=H\cdot W\cdot L \\ V=3x\cdot5x\cdot7x \\ V=105x^3 \end{gathered}[/tex]As x is the side of the little cube, x^3 is the volume of the little cube.
Knowing that x=0.5 in, we can calculate the volume of the little cube as:
[tex]V_l=x^3=(\frac{1}{2})^3=\frac{1}{8}in^3[/tex]Then, we can calculate the volume of the prism as:
[tex]V=105x^3=105\cdot V_l=105\cdot\frac{1}{8}=\frac{104}{8}+\frac{1}{8}=13+\frac{1}{8}[/tex]Answer: The volume of the prism is 13 1/8 cubic inches
