Answer
The Dutch boy must exert a force of $13.1~N$
Work Step by Step
We can find the pressure at a depth of 3.0 m under the water surface:
$P_{abs} = P_{atm}+P_g$
$P_{abs} = P_{atm}+\rho~gh$
$P_{abs} = (1.01\times 10^5~N/m^2)+(1025~kg/m^3)(9.80~m/s^2)(3.0~m)$
$P_{abs} = 1.31\times 10^5~N/m^2$
We can find the force the Dutch boy must exert:
$F = P~A$
$F = (1.31\times 10^5~N/m^2)~(1.0\times 10^{-4}~m^2)$
$F = 13.1~N$
The Dutch boy must exert a force of $13.1~N$.
