Discussion

Three solid metallic balls of diameter 3 cm, 4 cm and 5 cm are melted into a single solid sphere. The radius of the new sphere is

Answer: C

Melting conserves volume, and every sphere's volume is proportional to \( r^{3} \), so the \( \tfrac{4}{3}\pi \) cancels throughout.

The radii are 1.5, 2 and 2.5 cm:

\[ R^{3} = 1.5^{3} + 2^{3} + 2.5^{3} = 3.375 + 8 + 15.625 = 27 \]

\[ R = \sqrt[3]{27} = 3 \text{ cm} \]

Radii add in the cube, never directly: \( 1.5 + 2 + 2.5 = 6 \) is the first distractor and is far too large.

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