An illustration with 6 cubes packed in a right rectangular prism. If the edge of each cube measures 1/2 an inch, what is the volume of the whole rectangular prism?

Answer 1

Each cube has a volume of $(1/2)^3=1/8$ cubic inches. Since there are 6 cubes, their total volume is $6\times (1/8)=3/4$ cubic inches.

Let the dimensions of the rectangular prism be $l$, $w$, and $h$. Then we know that $lw=3/2$ and $h=3/2$. Therefore, the volume of the rectangular prism is $V=lwh=(3/2)(3/2)(3/2)=27/8$ cubic inches.