Will it float ?

The total volume of a brass spherical casing is given by:

$\displaystyle V = \frac{1}{6} \pi (d^{3}_{1} - d^{3}_{2}) \approx \frac{1}{6} \pi \times 169.4 \approx 88.69 \space \text{cm}^{3}$

The weight of the hollow sphere will be:

$G = 754 \space \text{g} = 0.754 \space \text{kg}$

The floating resp. sinking of the sphere can be seen from the Archimedes' principle, i.e - The equilibrium while floating appears when the weight of water displaced by the object is equal to the weight of the floating object.

That means that the weight of water, which would be displaced by the object would need to be greater than $G = 754 \space \text{g}$ and the displaced volume of water therefore $V_{v} = 754 \space \text{cm}^{3}$ . But because the total volume of the sphere is $V_{s} = 523.6 \space \text{cm}^{3}$ , the condition for floating isn't satisfied and therefore $\boxed{\text{the sphere will sink}}$ .