Answer:
[tex]5.3\ ft^3[/tex]
Step-by-step explanation:
Similar shapes with scale factor [tex]k[/tex] have proportional volumes with coefficient [tex]k^3[/tex] i.e.
[tex]\dfrac{V_{large}}{V_{small}}=k^3,[/tex]
where
[tex]k=\dfrac{\text{width of large prism}}{\text{width of small prism}}.[/tex]
Since
[tex]\text{width of large prism}=51\ ft,\\ \\\text{width of small prism}=17\ ft,[/tex]
then
[tex]k=\dfrac{51}{17}=3.[/tex]
Hence,
[tex]\dfrac{144}{V_{small}}=3^3\Rightarrow V_{small}=\dfrac{144}{27}=\dfrac{16}{3}=5\dfrac{1}{3}\approx 5.3\ ft^3.[/tex]
