#### Answer

The correct answer is:
(a) $1\times 10^{-3}~m^3$

#### Work Step by Step

Since the weight is $10~N$ less in the water, the buoyant force in the water is $10~N$. The buoyant force is equal to the weight of the water displaced by the brick. Note that $10~N$ of water has a mass of $1.0~kg$. We can find the volume of $1.0~kg$ of water:
$V = \frac{m_w}{\rho_w}$
$V = \frac{1.0~kg}{1000~kg/m^3}$
$V = 1\times 10^{-3}~m^3$
Since the volume of the brick is equal to the volume of the water that was displaced, the volume of the brick is $~1\times 10^{-3}~m^3$
The correct answer is:
(a) $1\times 10^{-3}~m^3$