The dimensions of a rectangular prism are shown below. Length 1 1/3 feet Width 1 foot length 2 1/3 feet. The lengths of the sides of a small cube are 1/3 foot each. How many small cubes can be packed in the rectangular prism?

Accepted Solution

Answer:84 cubesStep-by-step explanation:Given,The dimension of the rectangular prism are,[tex]1\frac{1}{3}\text{ ft }\times 1\text{ ft }\times 2\frac{1}{3}\text{ ft }[/tex]Hence, the volume of the prism,[tex]V=1\frac{1}{3}\times 1\times 2\frac{1}{3}[/tex][tex]=\frac{4}{3}\times \frac{7}{3}[/tex][tex]=\frac{28}{9}\text{ cube ft}[/tex]Now, the volume of a cube = side³,If side = [tex]\frac{1}{3}[/tex] ft,Then the volume of each cube,[tex]V'=(\frac{1}{3})^3=\frac{1}{27}\text{ cube ft}[/tex]Hence, the number of cubes that can be packet in the prism[tex]=\frac{V}{V'}[/tex][tex]=\frac{28/9}{1/27}[/tex][tex]=\frac{27\times 28}{9}[/tex][tex]=3\times 28[/tex][tex]=84[/tex]