Multiple choice

A solid sphere of radius 3 cm is melted to form a hollow cylinder of height 4 cm and external diameter 10 cm. What is the thickness of the cylinder?

  1. 0.42 cm

  2. 0.46 cm

  3. 0.50 cm

  4. 1.00 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The volume of the sphere is (4/3) * pi * 3^3 = 36 * pi. The volume of the hollow cylinder is pi * (R^2 - r^2) * h, where R = 5 cm (external radius) and h = 4 cm. Thus, 36 * pi = pi * (25 - r^2) * 4, which simplifies to 9 = 25 - r^2, so r^2 = 16 and r = 4 cm. The thickness is R - r = 5 - 4 = 1 cm.

AI explanation

Using the volume conservation formula, the volume of the solid sphere equals the volume of the hollow cylinder. The volume of the sphere is 4 divided by 3 times pi times 3 cubed, which equals 36 pi. The hollow cylinder has a height of 4 centimeters and an external radius of 5 centimeters; equating its volume to the sphere's gives 36 pi equals pi times 4 times (25 minus r squared). Solving for the inner radius squared gives r squared equals 16, so the inner radius is 4 centimeters. The thickness is the difference between the external radius and the inner radius, which is 5 minus 4, resulting in 1.00 centimeter.

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