Length: 1feetWidth: 1 footHeight: 2. feetThe lengths of the sides of a small cube foot each.Part A: How many small cubes can be packed in the rectangular prism? Show your work. (5 points)Part B: Use the answer obtained in part A to find the volume of the rectangular prism in terms of the small cube and a unit cube. (5 points)

Respuesta :

[tex]\begin{gathered} \text{volume of the rectangular prism=1x1x2=2} \\ \text{volume of the smal cube=1x1x1=1} \\ we\text{ can compare these volumes with the ratio:} \\ \frac{\text{volume of the rectangular prism}}{\text{volume of the small cube}}=\frac{2}{1}=2 \\ \text{hence, 2 small cube can be packed in the rectangular prism} \end{gathered}[/tex][tex]\begin{gathered} \text{from the ratio, we can s}e\text{ that:} \\ \frac{\text{volume of the rectangular prism}}{\text{volume of the small cube}}=2\Rightarrow\text{volume of the rectangular prism}=2\cdot\text{volume of the small cube} \\ \text{that is, the volum of the rectangular prism is 2 times the volume of the unit (small) cube} \end{gathered}[/tex]