Question

Calculate the volume of the solid. Please avoid decimals and leave your answer as a mixed fraction (e.g. 12 3/4) or improper fraction (e.g. 51/4).

Answer 1

Volume of the given solid is
`14(2)/(9)` cubic yds.

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

=
`(1* 1(1)/(3)* (2)/(3) )+[6* (4-1(1)/(3))* (2)/(3)]+(3* 1(1)/(3)* (2)/(3))`

=
`(8)/(9)+(6* (8)/(3)* (2)/(3))+(8)/(3)`

=
`(8)/(9)+(32)/(3)+(8)/(3)`

=
`(8)/(9)+(40)/(3)`

=
`(8)/(9)+(120)/(9)`

=
`(128)/(9)`

=
`14(2)/(9)`

Volume of the given solid is
`14(2)/(9)` cubic yds.