Question

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

• A. $12\%$
• B. $14\%$
• C. $7\%$
• D. $9\%$

Answer 1

The correct option is D $9\%$

Density $d=\frac{Mass}{Volume}$

Or $d=\frac{m}{a^3}$

Percentage error in density %$d=$ %$m+3\times$ % $a$

$⟹$ %$d=3+3\times 2=9$ %