Melting Copper Wire to Sphere

CMAT 2022 · Quantitative Techniques & Data Interpretation · Medium · Mensuration

A copper wire having length of 243 m and diameter 4 mm was melted to form a sphere. Find the diameter of the sphere:

  1. A.

    17 m

  2. B.

    18 cm

  3. C.

    15 cm

  4. D.

    20 cm

Answer

B

Explanation

Wire is cylindrical with length h=243 m=24300 cmh = 243\text{ m} = 24300\text{ cm} and radius r=2 mm=0.2 cm=210 cmr = 2\text{ mm} = 0.2\text{ cm} = \frac{2}{10}\text{ cm}. Volume of cylindrical wire =πr2h=π(210)2×24300=972π cm3= \pi r^2 h = \pi \left(\frac{2}{10}\right)^2 \times 24300 = 972\pi\text{ cm}^3. Volume of sphere =43πR3=972π= \frac{4}{3}\pi R^3 = 972\pi. R3=972×34=729  ⟹  R=9 cmR^3 = 972 \times \frac{3}{4} = 729 \implies R = 9\text{ cm}. Diameter =2R=18 cm= 2R = 18\text{ cm}.

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