The diameter of the largest sphere that can be obtained from the cone will be 21 cm. Radius of the cone = \(\frac{21}{2}\) cm Radius of the sphere = \(\frac{21}{2}\) cm ∴ Ratio of the volumes of the cone and the sphere: \[ = \pi \left(\frac{21}{2}\right)^2 \times 21 : \frac{4}{3} \pi \left(\frac{21}{2}\right)^3 \] \[ = \frac{\pi \times 21 \times 21 \times 21}{2 \times 2} : \frac{4\pi \times 21 \times 21 \times 21}{3 \times 2 \times 2 \times 2} \] \[ = 1 : \frac{4}{6} \] \[ = 6 : 4 \] \[ = 3 : 2 \] ∴ The ratio of the volumes of the cone and the sphere is 3:2.