What length of wire with a 0.2 mm radius can be drawn from a melted solid copper sphere of 18 cm diameter?
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Answer: D. 24300 m
Explanation
Equating the volume of the melted copper sphere to the volume of the cylindrical wire allows solving for length. Sphere volume is calculated using four-thirds pi radius cubed with a diameter of eighteen centimeters. Cylinder volume uses pi radius squared with a zero point two millimeter radius yielding twenty four thousand three hundred meters. Conservation of volume dictates that melting a solid shape and reshaping it preserves total material volume. Sphere volume formula requires radius cubed while cylinder volume requires radius squared multiplied by height. Unit conversions between millimeters and meters are essential before finalizing length calculations.
Metallurgical manufacturing processes calculate wire drawing lengths from cast metal ingots and spheres. Industrial extrusion applications rely on volume conservation to determine finished product dimensions. Understanding three-dimensional volume formulas is crucial in materials science and engineering. Option A suggests twenty four point three meters which underestimates the wire length calculation. Option B suggests two hundred forty three meters which misses a factor of ten in unit conversion. Option C suggests two thousand four hundred thirty meters which is ten times shorter than the correct result.
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- Mathematics
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- Mathematics
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