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

Answer:

Volume of the given solid is $14\frac{2}{9}$ 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

                                 = $(1\times 1\frac{1}{3}\times \frac{2}{3} )+[6\times (4-1\frac{1}{3})\times \frac{2}{3}]+(3\times 1\frac{1}{3}\times \frac{2}{3})$

                                 = $\frac{8}{9}+(6\times \frac{8}{3}\times \frac{2}{3})+\frac{8}{3}$

                                 = $\frac{8}{9}+\frac{32}{3}+\frac{8}{3}$

                                 = $\frac{8}{9}+\frac{40}{3}$

                                 = $\frac{8}{9}+\frac{120}{9}$

                                 = $\frac{128}{9}$

                                 = $14\frac{2}{9}$

Volume of the given solid is $14\frac{2}{9}$ cubic yds.