Radius of the cone = \(\cfrac{16}{2}\) cm = 8 cm Radius of each sphere = \(\cfrac{6}{2}\) cm = 3 cm Let \(x\) be the number of spheres to be dropped. So, Volume of \(x\) spheres = \(\cfrac{4}{3}\pi \times 3^3 \times x\) Volume of water displaced in the cone = \(\pi \times 8^2 \times 9\) Equating the two: \(\cfrac{4}{3}\pi \times 27 \times x = \pi \times 64 \times 9\) Solving, \(x = \cfrac{64 \times 9}{4 \times 27} = \cfrac{576}{108} = 16\) ∴ 16 spheres must be dropped.