I am looking at the start of the consider how to calculate the entropy of a monatomic ideal gas.

We need to determine the number of microstates in $E \leq \mathcal{H}(\Gamma) \leq E+\Delta$. The volume of the this region is $\omega(E,V,N)$. The Hamiltonian has the form

$$\mathcal{H}(\Gamma)=\sum_{i=1}^{3N}\frac{p_i^2}{2m} $$

where the position coordinates restricted to box with volume $V$. The equation $\mathcal{H}(\Gamma)=E$ describes the hypersphere with radius $\sqrt{2mE}$. Thus

$$\omega(E,V,N)=V^NS_{3N}(\sqrt{2mE})\Delta $$

How has this last formula been found?