Answer :
Given the dimensions of the carton:
[tex]\begin{gathered} l=2\frac{2}{3}ft \\ \\ w=1\frac{1}{8}ft \\ \\ h=1\frac{1}{3}ft \end{gathered}[/tex]You can convert them to Improper Fractions as follows:
- Multiply the whole number part by the denominator.
- Add the result to the numerator.
- The denominator does not change.
Then:
[tex]2\frac{2}{3}=\frac{(2\cdot3)+2}{3}=\frac{6+2}{3}=\frac{8}{3}\Rightarrow l=\frac{8}{3}ft[/tex][tex]1\frac{1}{8}=\frac{(1\cdot8)+1}{8}=\frac{9}{8}\Rightarrow w=\frac{9}{8}ft[/tex][tex]1\frac{1}{3}=\frac{(1\cdot3)+1}{3}=\frac{4}{3}\Rightarrow h=\frac{4}{3}ft[/tex]Now you need to use the following formula for calculating the volume of a rectangular prism:
[tex]V=l\cdot w\cdot h[/tex]Where "l" is the length, "w" is the width and "h" is the height.
Then, substituting values into the formula and evaluating, you get:
[tex]V=(\frac{8}{3}ft)(\frac{9}{8}ft)(\frac{4}{3}ft)[/tex][tex]\begin{gathered} V=(\frac{8\cdot9\cdot4}{3\cdot8\cdot3})ft^3 \\ \\ V=\frac{288ft^3}{72} \end{gathered}[/tex][tex]V=4ft^3[/tex]Hence, the answer is:
[tex]V=4ft^3[/tex]