Let (mathcal{S}_{1}) be the closed surface consisting of (mathcal{S}) in Figure 18 together with the unit disk.

Question:

Let $\mathcal{S}_{1}$ be the closed surface consisting of $\mathcal{S}$ in Figure 18 together with the unit disk. Find the volume enclosed by $\mathcal{S}_{1}$, assuming that
\[
\iint_{\mathcal{S}_{1}}\langle x, 2 y, 3 zangle \cdot d \mathbf{S}=72
\]

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