The following data is given for calculating density of cylinder
Mass=$6.7\pm 0.1 g$
Radius=$0.087\pm 0.001 cm$
Length=$3.28\pm 0.01 cm$
MY SOLUTION-
Let density by d
$$\frac{\Delta d}{d}=\frac{\Delta m}{m}+\frac{\Delta l}{l} + \frac{2\Delta r}{r}$$
Plugging in the values, we end up with something around 4.69%. The answer is 2.4%.
I have seen the solution for this question, and in that, they took the original equation as
$$\frac{\Delta d}{d}=\frac{\Delta m}{m}+ \frac{\Delta r}{2r} + \frac{\Delta l}{l}$$
The main difference in the both solutions is the denominator of the relative error in radius. As far as I know, we multiple the powers in the numerator. So why did they take it like that?
Your equation for the error in the density is correct. The $2$ should be in the numerator of the radius term because the factor in the volume is $r^2$. I get about $4.096\%$ error (though I would report fewer decimals, I show them for comparison). The solution manual is wrong in the equation, then evaluates it correctly.