Multiple choice

If a cylinder of radius 3 cm and height 10 cm is melted and recast into the shapes of small spheres of diameter 1 cm, then the number of spheres so formed is

  1. 132

  2. 270

  3. 540

  4. 1080
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cylinder = π * 3^2 * 10 = 90π. Volume of one sphere = (4/3) * π * (0.5)^3 = (4/3) * π * 0.125 = π/6. Number of spheres = 90π / (π/6) = 540.

AI explanation

The volume of the cylinder is found using pi*r^2*h, which equals (22/7)3^2*10 = 1980/7 cm3. The volume of one small sphere with a diameter of 1 cm is (4/3)*pi(0.5)^3, which equals 11/21 cm3. Dividing the total volume of the cylinder by the volume of a single sphere gives (1980/7) / (11/21) = 540 spheres.

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