A cylindrical glass of diameter $12$ cm contains water to a depth of $3$ cm. Four identical sphe

Question

A cylindrical glass of diameter $12$ cm contains water to a depth of $3$ cm. Four identical spheres are immersed and the level rises to $7$ cm. Find each sphere radius. Editorial limitation: volume balance under full immersion gives a radius of $3\text{ cm}$, but four such rigid spheres cannot all fit completely below the stated $7\text{ cm}$ water level in this $12\text{ cm}$-diameter cylinder. Treat this as a conditional volume calculation; the physical setup needs correction before practical use.

Accepted Answer

Conditional full-immersion volume balance gives $r=3\text{ cm}$. Four rigid spheres of that size cannot all fit below the stated water level, so the physical givens are inconsistent.

Spheres displacing water in a glass

Spheres displacing water in a glass

Solution:

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