Step 1: Understand volume strength of $H_2O_2$.
Volume strength of hydrogen peroxide is defined as the volume (in litres) of oxygen liberated at NTP by one litre of the solution. Step 2: Relation between volume strength and strength in g L$^{-1$.
For hydrogen peroxide,
\[
\text{Strength (g L}^{-1}) = \text{Volume strength} \times 3.035
\] Step 3: Substitute the given value.
\[
\text{Strength} = 10 \times 3.035
\]
\[
\text{Strength} = 30.35\ \text{g L}^{-1}
\] Step 4: Conclusion.
The strength of 10 volume hydrogen peroxide solution is $30.35\ \text{g L}^{-1}$.