Multiple choice

A solid sphere of radius 3 cm is melted to form a hollow right circular cylindrical tube of length 4 cm and external radius 5 cm. The thickness of the tube is

  1. 1 cm

  2. 9 cm

  3. 0.6 cm

  4. 1.5 cm
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A Correct answer
Explanation

Volume of sphere = 4/3 * pi * 3^3 = 36 * pi. Volume of hollow cylinder = pi * h * (R^2 - r^2) = pi * 4 * (5^2 - r^2) = 4 * pi * (25 - r^2). Setting them equal: 36 = 4 * (25 - r^2), so 9 = 25 - r^2, r^2 = 16, r = 4. Thickness = R - r = 5 - 4 = 1 cm.

AI explanation

The volume of the solid sphere is calculated using the sphere volume formula, yielding (4/3) * pi * 3^3 = 36*pi. Let the thickness of the hollow cylinder be t, so its inner radius is (5 - t). Using the hollow cylinder volume formula, the volume of the metal is pi * 4 * (5^2 - (5 - t)^2) = 36*pi. Dividing by 4*pi gives 25 - (25 - 10t + t^2) = 9, which simplifies to 10t - t^2 = 9. Factoring yields (t - 1)(t - 9) = 0, and since the thickness must be less than the radius, the thickness is 1 cm.

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