Solution
Given the dimensions of a rectangular prism as
length: 1.5 ft
width: 1 ft
Height: 2.5 ft
Part A.
Volume of a rectangular prism =
[tex]\begin{gathered} V_{RP}=l\times w\times h \\ \\ l\text{ is the length} \\ \\ w\text{ is the width} \\ \\ h\text{ is the height} \end{gathered}[/tex][tex]V_{RP}=1.5\times1\times2.5=3.75\text{ ft}^3[/tex]Volume of small cubes
[tex]V_{SC}=0.5^3=0.125\text{ ft}^3[/tex]Number of small cubes that can be packed in a rectangular prism is 30
[tex]N=\frac{V_{RP}}{V_{SC}}=\frac{3.75}{0.125}=30[/tex]Hence, there are 30 small cubes that can be packed in the rectangular box.
Part B.
The volume is given as
[tex]\sqrt[3]{30}=3.12[/tex]