Question

if the error involved in the measurement of a side and mass of a cube are 3% and 4% respectively. what is the maximum error

Answer 1

Formula is delta of (density) = (delta of (mass) /mass} + { 3 * delta of (length)/ length) .

Substitute the values in the above equation. i.e l = 3%, m = 4%, 


=  delta of (density) * 100 = 4 % + 3 * (3%)

                                           = 4% + 9%

                                           = 13%

So, Maximum Error = 13%.


Hope this helps!

Answer 2

Formula for the error in density is given by

$\Delta \rho \% = \frac{\Delta m}{m}\%+[3*\frac{\Delta L}{L} \%]$

here,  $\Delta \rho \%$ is the percentage change in density of the cube

          $\frac{\Delta m}{m}\%$ is the percentage change in mass of the cube

          $[3* \frac{\Delta L}{L}]\%$ is the percentage change in volume of the cube

Note: since the volume is '$L^3$' then the percent error would be '3 folds the length error' that's why 'multiplying 3' with length error gives us the volume error.

Therefore the error in the density or the maximum error would be

$\Delta \rho \% = 4\%+[3*3\%]\\\Delta \rho \% = 13\%$

is the required answer

#SPJ2