A cylindrical vessel of radius 8 cm is partially filled with water. By how much will the water level rise if a sphere of radius 7 cm is completely immersed in this water?
Radius of sphere, R = 7 cm
Radius of cylinder, r = 8 cm and height of cylinder = h cm
The rise in water level is equal to the height of cylinder when volumes of both solids is equal.
=> Volume of cylinder = Volume of sphere
=> $$\pi r^2 h = \frac{4}{3} \pi R^3$$
=> $$(8)^2 \times h = \frac{4}{3} \times (7)^3$$
=> $$h = \frac{343}{16 \times 3} = 7.15$$ cm
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