Radius of each marble $r = \dfrac{1.4}{2} = 0.7$ cm
Volume of 150 marbles $= 150 \times \dfrac{4}{3}\pi r^3 = 150 \times \dfrac{4}{3} \times \dfrac{22}{7} \times (0.7)^3$
$= 150 \times \dfrac{4}{3} \times \dfrac{22}{7} \times 0.343 = 154$ cm³
Radius of cylindrical vessel $R = \dfrac{7}{2} = 3.5$ cm
Let rise in water level $= h$
Volume of water displaced $=$ Volume of marbles
$\pi R^2 h = 154$
$\dfrac{22}{7} \times 3.5 \times 3.5 \times h = 154$
$38.5 \times h = 154$
$h = \dfrac{154}{38.5} = 4$ cm
The rise in the level of water = 4 cm.
Source: Surface Areas and Volumes, Section 12.3
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The key concept is volume conservation: volume of water raised = total volume of marbles submerged. Use $V_{\text{sphere}} = \dfrac{4}{3}\pi r^3$ and $V_{\text{cylinder}} = \pi R^2 h$, then equate them. Examiners expect clear working for each step and the final answer with units.