A lead spherical mass measuring 3 cm across is melted down and re-formed into 3 distinct spherical masses. Two of these measure 1 ½ cm and 2 cm in diameter respectively. What is the diameter of the third mass?
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Answer: B. 2.5 cm
Explanation
The volume of a sphere is proportional to the cube of its diameter using standard geometry. Subtracting the cubed diameters of the two smaller spheres from the original sphere cube leaves fifteen point six two five. Extracting the cube root of fifteen point six two five determines the third sphere diameter as two point five. Melting and reshaping solid objects conserves the total volume of material across transformations. Sphere volumes scale cubically with respect to their linear diameter or radius dimensions. Cube root calculations determine linear dimensions from known volumetric measurements.
Metallurgical manufacturing relies on volume conservation principles when recasting metal spheres. Materials science applies scaling laws to understand how particle sizes affect surface area to volume ratios. Sculpting and casting processes require calculating material volumes to ensure successful molds. Option A suggests two point sixty six centimeters which rounds the cube root incorrectly. Option C proposes three centimeters which incorrectly implies the third sphere is identical to the first. Option D offers three point five centimeters which overstates the remaining volume capacity.
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- Mathematics
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- Mathematics
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