Question

The density of the material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively $1.5\%$ and $1\%$, the maximum error in determining the density is:

• A. $4.5\%$
• B. 6%
• C. $2.5\%$
• D. $3.5\%$

Answer 1

The correct option is A

$4.5\%$

Explanation for the correct answer:

To find the maximum error in determining the density.

The density formula is $\rho =\frac{m}{V}$where $m$is the mass and $V$ is the volume.

Then the maximum error in the density formula is $\frac{∆\rho }{\rho }=\frac{∆m}{m}+3\frac{∆l}{l}$

$=1.5+3\times 1$

$=4.5$

Hence maximum error in density is $4.5$

Therefore, Option (A) is the correct