Multiple choice

In a workshop, an aluminum sphere with a radius of 6 cm is melted and recast into a cylindrical rod with a height of 32 cm. What is the diameter of the cylindrical rod?

  1. 2 cm

  2. 3 cm

  3. 5 cm

  4. 6 cm

  5. a
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of sphere = 4/3 * pi * r^3 = 4/3 * pi * 6^3 = 4/3 * pi * 216 = 288 * pi. Volume of cylinder = pi * r_cyl^2 * h = pi * r_cyl^2 * 32. 288 * pi = 32 * pi * r_cyl^2 => r_cyl^2 = 288 / 32 = 9. r_cyl = 3. Diameter = 2 * 3 = 6 cm.

AI explanation

Because the sphere is melted and recast, the volume of the sphere equals the volume of the cylindrical rod. Using the volume of a sphere formula, 4/3 times pi times r cubed, we get 4/3 times pi times 6 cubed, which equals 288 pi cubic cm. Setting this equal to the volume of the cylinder, pi times r squared times height, we have 288 pi equals pi times r squared times 32, which gives r squared equals 9, so the radius is 3 cm and the diameter is 6 cm.

Keep practicing — related questions