First, let us write down the chemical equation for this reaction.

`2 KOH + H_2SO_4 -> K_2SO_4 + 2 H_2O`

From the balanced chemical equation, we can see that 2 moles of KOH is needed to react 1 mole of H2SO4. 

First, we need to get the moles of H2SO4:

`Mol es H_2SO_4 = (15.0)/(1000) L * 0.350M`

`Mol es H_2SO_4 = 0.00525 mol es H_2SO_4`

From the balanced equation:

`0.00525 mol es H_2SO_4 * (2 mol es KOH)/(1 mol e H_2SO_4)`

= 0.0105 moles KOH

Finally, to get the volume, we need the expression for molarity:

`Molarity = (mol es solute)/(Volume of Solution(L))`

`Volume of solution = (Mol es KOH)/(Molarity)`

`Volume of solution = (0.0105)/(0.250)`

Volume of solution = 0.042 L = 42 mL **

** 1000mL = 1L