Question

The Density of Metal is 7.56 g/cm³. Change the SI Unit into kg/m³​

Answer 1

Answer:

• Density of Metal = 7.56 g/cm³

$\bf{\dag}\:\underline{\sf we\:know\:that :}\\\bullet\:\sf1\:gram=\dfrac{1}{1000}\:kg=10^{-3}\:kilogram\\\\ \bullet\:\sf1\:cm=\dfrac{1}{100}\:m=10^{-2}\:metre$

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$\underline{\bigstar\:\textbf{According to the Question :}}$

$:\implies\sf 7.56\:g/cm^3=7.56\:g\:cm^{-3}\\\\\\:\implies\sf 7.56\:g/cm^3= 7.56 \times (10^{ - 3} \:kg) \times (10^{ -2}\:m)^{ - 3}\\\\\\:\implies\sf 7.56\:g/cm^3= 7.56 \times (10^{ - 3} \:kg) \times (10^6 \:m^{ - 3})\\\\\\:\implies\sf 7.56\:g/cm^3= 7.56 \times (10^{ - 3} \times 10^6)\:kg\:m^{ - 3}\\\\\\:\implies\sf 7.56\:g/cm^3= 7.56 \times 10^{(-3 + 6)}\:kg\:m^{ - 3}\\\\\\:\implies\sf 7.56\:g/cm^3= 7.56 \times 10^3\:kg\:m^{ - 3}\\\\\\:\implies\sf 7.56\:g/cm^3= \dfrac{756}{100} \times 1000\:kg\:m^{ - 3}\\\\\\:\implies\sf 7.56\:g/cm^3=756 \times 10\:kg\:m^{ - 3}\\\\\\:\implies\underline{\boxed{\sf7.56\:g/cm^3= 7560\:kg/m^3}}$

⠀

$\therefore\:\underline{\textsf{Required value of this will be \textbf{7560 kg/m ^ \text3 }}}.$

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⠀⠀⠀⠀⠀Conversion Table

$\begin{tabular}{|c|c|c|}\cline{1-3} \sf Length &\sf Prefix &\sf Symbol\\\cline{1-3}\sf 10^{3}&\sf Kilo &\sf km/kg\\\cline{1-3} \sf 10^{2}&\sf Hecto & \sf hm/hg\\ \cline{1-3} \sf 10&\sf Deca &\sf dam/dag\\\cline{1-3} \sf 1&\sf Metre &\sf m/g\\ \cline{1-3} \sf 10^{-1}&\sf Deci &\sf dm/dg\\\cline{1-3} \sf 10^{-2}&\sf Centi & \sf cm/cg\\ \cline{1-3}\sf 10^{-3}&\sf Mili& \sf mm/mg\\\cline{1-3}\end{tabular}$