Question

Whats the maxium volume that hold 1 2/3 inches and length of 2 1/3 and width of 2 inches

Answer 1

so a box will be a rectangular prism, and thus its volume will simply be the product of its length, width and height.

let's firstly convert the mixed fractions to improper fractions and the multiply.

`\bf \stackrel{mixed}{1(2)/(3)}\implies \cfrac{1\cdot 3+2}{3}\implies \stackrel{improper}{\cfrac{5}{3}}~\hfill \stackrel{mixed}{2(1)/(3)}\implies \cfrac{2\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{7}{3}} \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a rectangular prism}\\\\ V=Lwh~~ \begin{cases} L=(7)/(3)\\ w=2\\ h=(5)/(3) \end{cases}\implies V=\cfrac{7}{3}\cdot 2\cdot \cfrac{5}{3}\implies V=\cfrac{70}{9}\implies V=7(7)/(9)`