Volume of the hollow cylinder = \[ \pi (5^2 - 4^2) \times 20 \text{ cubic cm} = \pi \times (25 - 16) \times 20 = \pi \times 9 \times 20 = 180\pi \text{ cubic cm} \] Height of the solid cone = \[ \frac{20}{3} \text{ cm} \] Let the radius of the base of the cone be \(r\) cm. Then, volume of the cone = \[ \frac{1}{3} \pi r^2 \times \frac{20}{3} = 180\pi \] Solving: \[ \frac{20}{9} r^2 = 180 \Rightarrow r^2 = 180 \times \frac{9}{20} = 81 \Rightarrow r = \pm 9 \] Since radius cannot be negative, the base radius of the cone is 9 cm. Therefore, the diameter of the base of the cone = \(9 \times 2 = 18\) cm.