#### Answer

The mass of the heaviest rock that will not sink the boat is 0.11 kg

#### Work Step by Step

We can find the volume of water that would be displaced by the hemisphere.
$V = \frac{2}{3}\pi~r^3$
$V = \frac{2}{3}\pi~(0.040~m)^3$
$V = 1.34\times 10^{-4}~m^3$
The maximum possible buoyant force on the hemisphere is equal to the weight of water displaced by the entire volume of the hemisphere. To find the mass of the heaviest rock, we can assume that the total weight of the boat and the rock is equal to the maximum possible buoyant force.
$M_{boat}~g+M_{rock}~g = \rho~V~g$
$M_{rock} = \rho~V-M_{boat}$
$M_{rock} = (1000~kg/m^3)(1.34\times 10^{-4}~m^3)-(0.021~kg)$
$M_{rock} = 0.11~kg$
The mass of the heaviest rock that will not sink the boat is 0.11 kg.