Answer:
Volume of the given solid is [tex]14\frac{2}{9}[/tex] cubic yds.
Step-by-step explanation:
Solid given in the figure is a composite structure made up with three rectangular prisms.
Formula to used,
Volume of a rectangular prism = length × width × height
Volume of the solid = Volume of all rectangular prisms
= [tex](1\times 1\frac{1}{3}\times \frac{2}{3} )+[6\times (4-1\frac{1}{3})\times \frac{2}{3}]+(3\times 1\frac{1}{3}\times \frac{2}{3})[/tex]
= [tex]\frac{8}{9}+(6\times \frac{8}{3}\times \frac{2}{3})+\frac{8}{3}[/tex]
= [tex]\frac{8}{9}+\frac{32}{3}+\frac{8}{3}[/tex]
= [tex]\frac{8}{9}+\frac{40}{3}[/tex]
= [tex]\frac{8}{9}+\frac{120}{9}[/tex]
= [tex]\frac{128}{9}[/tex]
= [tex]14\frac{2}{9}[/tex]
Volume of the given solid is [tex]14\frac{2}{9}[/tex] cubic yds.
