Let the number of bottles required be \( x \). Volume of the hemispherical vessel = \( \frac{2}{3} \pi \times 9^3 \) cubic cm Radius of each bottle = \( \frac{3}{2} \) cm ∴ Volume of each bottle = \( \pi \times \left(\frac{3}{2}\right)^2 \times 4 \) cubic cm According to the question: \[ \pi \times \left(\frac{3}{2}\right)^2 \times 4 \times x = \frac{2}{3} \pi \times 9^3 \] Simplifying: \[ \frac{9}{4} \times 4 \times x = \frac{2}{3} \times 729 \] \[ 9x = 486 \] \[ x = 54 \] ∴ 54 bottles are required.