7. 16 .

Compare the upper half of the geometric solid obtained from the problem with a hemisphere of radius 16, placing their bases on the same horizontal plane, and examine the cross-sectional areas at a height of $h$ from the two solids. The cross-section formed by the first solid is an annulus, with an outer radius of $\sqrt{20-h^{2}}$ and an inner radius of 12, so the area is $\pi\left(20^{2}-h^{2}-12^{2}\right)=\pi\left(16^{2}-h^{2}\right)$, which is precisely the area of the circular cross-section formed by the second hemisphere. According to Zu Chongzhi's principle, the volumes of the two solids are equal.
7. As shown in Figure 1, there is a solid metal sphere with a radius of 20. A circular hole with a radius of 12 is drilled along a certain diameter as the central axis, and the remaining part is melted and cast into a new solid sphere. What is the radius of the new sphere? $\qquad$