The volume of a sphere with radius 1 cm \[ = \frac{4}{3}\pi \times 1^3 \text{ cubic cm} = \frac{4}{3}\pi \text{ cubic cm} \] The volume of a sphere with radius 6 cm \[ = \frac{4}{3}\pi \times 6^3 \text{ cubic cm} = \frac{4}{3}\pi \times 216 \text{ cubic cm} \] ∴ Volume of the new sphere \[ = \frac{4}{3}\pi + \frac{4}{3}\pi \times 216 = \frac{4}{3}\pi \times 217 \text{ cubic cm} \] Let the inner radius of the hollow sphere be \( r \) cm ∴ Volume of the hollow sphere \[ = \frac{4}{3}\pi (9^3 - r^3) \text{ cubic cm} \] According to the question, \[ \frac{4}{3}\pi (9^3 - r^3) = \frac{4}{3}\pi \times 217 \] Or, \[ 9^3 - r^3 = 217 \] Or, \[ 729 - r^3 = 217 \] Or, \[ r^3 = 729 - 217 = 512 \] Or, \[ r^3 = 8^3 \Rightarrow r = 8 \] ∴ The inner radius of the new hollow sphere is 8 cm.