Let \(x\) be the number of spheres required to raise the water level by 2 cm in the conical vessel. Each solid sphere with radius 1.5 cm has a volume of \[ \frac{4}{3} \pi (1.5)^3 \text{ cubic cm} \] According to the question, \[ \frac{4}{3} \pi (1.5)^3 \times x = \pi \times 6^2 \times 2 \] Or, \[ \frac{4}{3} \times \frac{15 \times 15 \times 15}{10 \times 10 \times 10} \times x = 36 \times 2 \] Solving, \[ x = \frac{36 \times 2 \times 3 \times 10 \times 10 \times 10}{4 \times 15 \times 15 \times 15} \] \[ x = 16 \] ∴ To raise the water level by 2 cm in the conical vessel, 16 spheres are required.