Question

The density of the material of a cube is measured by measuring its mass and length of its side. If the maximum error in the measurement of mass and the length are $3\%$ and $2\%$ respectively, the maximum error in the measurement of density is

• A. $1\%$
• B. $5\%$
• C. $7\%$
• D. $9\%$

Answer 1

The correct option is D $9\%$

$\text{Density}\rho =\frac{\text{mass}}{\text{volume}}=\frac{m}{V}$
Let the length of each side of the cube be $l$.

$V=l^3$
$\rho =\frac{m}{l^3}$

Net % error $=1\times 3$%$+3\times 2$%$=9$%