The answer is #280 cm^3#.

A solution's percent concentration by mass is defined as the mass of the solute divided by the mass of the solution and multiplied by 100%.

#c = m_(solute)/m_(solution) * 100%#, where #m_(solution) = m_(solvent) + m_(solute)#.

We know that #m_(solution1) = 70g# and the the concentration is equal to #c_1 = 10%#, which means we can determine the mass of #KCl# used for the mixture

#m_(KCl) = (c_1 * m_(solution))/100 = (10 * 70)/100 = 7g#

Now, let's say that after adding a certain mass of water - #m_(added)# - we would get a new concentration of #c_2 = 2%#. This means that

#c_2 = m_(KCl)/m_(solution2) * 100#, where

#m_(solution2) = m_(solutiuon1) + m_(added)#

Therefore, #m_(solution2) = (m_(KCl) * 100)/c_2 = 7 * 100/2 = 350g#

This means that #m_(added) = m_(solution2) - m_(solution1) = 350 - 70 =280g#

Assuming we're at room temperature, we can determine the volume of water by using its known density of #rho = 1g/(cm^3)#

#V_(water) = m_(added)/rho = (280g)/(1 g/(cm^3)) = 280 cm^3#