Question

Billy has 1 gallon of paint he is going to pour it into a paint tray that measures 10 in wide 14 in long 4 cm deep. 1 gallon=231 in cubed 1 in=2.54 cm what will happen

Answer 1

well, the tray is 10"x14"x4cm ok.... let's convert the centimeters to inches then


`\bf \begin{array}{ccllll} inches&cm\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ 1&2.54\\ x&4 \end{array}\implies \cfrac{1}{x}=\cfrac{2.54}{4}\implies \boxed{\cfrac{4}{2.54}=x} \\\\\\ \textit{thus, the volume of the tray, which is a rectangular prism, is}\\\\ V=length\cdot width\cdot height\implies V=10in\cdot 14in\cdot \cfrac{4}{2.54}in \\\\\\ V\approx 220.47244\ in^3`

now, we know 1gallon is 231in³... how many gallons then, are there in 220.47244 in³?


`\bf \begin{array}{ccllll} gallon&in^3\\ \textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\\ 1&231\\ x&220.47244 \end{array}\implies \cfrac{1}{x}=\cfrac{231}{220.47244}\implies \cfrac{220.47244}{231}=x`

now, he's going to pour 1gallon of paint on this tray, will the tray take up the whole gallon?