Convert ton / cubic inch to pound / cubic foot
Learn how to convert
1
ton / cubic inch to
pound / cubic foot
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{ton}{cubic \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{cubic \text{ } foot}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{ton}{cubic \text{ } inch}\right) = {\color{rgb(89,182,91)} \dfrac{10^{3}}{1.6387064 \times 10^{-5}}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(89,182,91)} \dfrac{10^{3}}{1.6387064 \times 10^{-5}}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{pound}{cubic \text{ } foot}\right) = {\color{rgb(125,164,120)} \dfrac{5.0}{0.28316846592}\left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(125,164,120)} \dfrac{5.0}{0.28316846592}\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{ton}{cubic \text{ } inch}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{pound}{cubic \text{ } foot}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{3}}{1.6387064 \times 10^{-5}}} \times {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{5.0}{0.28316846592}}} \times {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} kilo}gram}{cubic \text{ } meter}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{10^{3}}{1.6387064 \times 10^{-5}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{5.0}{0.28316846592}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{10^{3}}{1.6387064 \times 10^{-5}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{5.0}{0.28316846592}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{{\color{rgb(230,179,255)} k}g}{m^{3}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{10^{3}}{1.6387064 \times 10^{-5}} = {\color{rgb(20,165,174)} x} \times \dfrac{5.0}{0.28316846592}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{5.0}{0.28316846592} = \dfrac{10^{3}}{1.6387064 \times 10^{-5}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{0.28316846592}{5.0}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{5.0}{0.28316846592} \times \dfrac{0.28316846592}{5.0} = \dfrac{10^{3}}{1.6387064 \times 10^{-5}} \times \dfrac{0.28316846592}{5.0}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{5.0}} \times {\color{rgb(99,194,222)} \cancel{0.28316846592}}}{{\color{rgb(99,194,222)} \cancel{0.28316846592}} \times {\color{rgb(255,204,153)} \cancel{5.0}}} = \dfrac{10^{3} \times 0.28316846592}{1.6387064 \times 10^{-5} \times 5.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{3} \times 0.28316846592}{1.6387064 \times 10^{-5} \times 5.0}\)
Rewrite equation
\(\dfrac{1.0}{10^{-5}}\text{ can be rewritten to }10^{5}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{5} \times 10^{3} \times 0.28316846592}{1.6387064 \times 5.0}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{8} \times 0.28316846592}{1.6387064 \times 5.0}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 3456000 = 3.456 \times 10^{6}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{ton}{cubic \text{ } inch}\right) = {\color{rgb(20,165,174)} 3.456 \times 10^{6}}\left(\dfrac{pound}{cubic \text{ } foot}\right)\)
