Multiple choice

A solid sphere of diameter 60 mm is melted to stretch into a wire of length 144 cm. What is the diameter of the wire?

  1. 0.5 cm

  2. 1 cm

  3. 1.5 cm

  4. 2 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of sphere = (4/3) * pi * r^3 = (4/3) * pi * 30^3 = 36000 * pi mm^3 = 36 * pi cm^3. Volume of wire (cylinder) = pi * r_w^2 * h = pi * r_w^2 * 144. Equating: 36 * pi = 144 * pi * r_w^2. r_w^2 = 36/144 = 1/4. r_w = 0.5 cm. Diameter = 2 * r_w = 1 cm.

AI explanation

The volume of the sphere is found using the formula four-thirds times pi times the radius cubed, where the 60 mm diameter gives a 3 cm radius, resulting in 36 * pi cubic centimeters. Equating this to the wire volume formula, pi times the radius squared times the height, gives 36 * pi = pi * r^2 * 144. Solving for r yields 0.5 cm, making the diameter 1 cm.

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