# In the density measurement of a cube, the mass and edge length are measured as $\left ( 10.00\pm 0.10 \right )kg$ and $\left ( 0.10\pm 0.01 \right )m,$ respectively. The error in the measurement of density is : Option 1)  $0.01\: kg/m^{3}$ Option 2)  $0.10\: kg/m^{3}$ Option 3) $0.31\: kg/m^{3}$ Option 4)  $0.07\: kg/m^{3}$

$Mass=\left ( 10.00\pm 0.10 \right )kg$

$Length=\left ( 0.10\pm 0.01 \right )m$

$Density=\frac{Mass}{Volume}=\frac{m}{a^{3}}$

$\rho =\frac{m}{a^{3}}$

$\frac{\Delta \rho}{\rho}=\frac{\Delta m}{m}+3\frac{\Delta a}{a}$

$=\frac{0.10}{10}+3\frac{\left( .01 \right )}{0.10}$

$=.01+.3$

$=0.31\: kg/m^{3}$

Option 1)

$0.01\: kg/m^{3}$

Option 2)

$0.10\: kg/m^{3}$

Option 3)

$0.31\: kg/m^{3}$

Option 4)

$0.07\: kg/m^{3}$

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