Multiple choice

The number of solid spheres each of diameter $6$ cm that could be moulded to form a solid metal cylinder of height $45$ cm and diameter $4$ cm is

  1. $3$
  2. $4$
  3. $5$
  4. $6$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * (2)^2 * 45 = 180 * pi. Volume of one sphere = (4/3) * pi * r^3 = (4/3) * pi * (3)^3 = 36 * pi. Number of spheres = 180 * pi / 36 * pi = 5.

AI explanation

The volumes of the cylinder and the spheres must be equal, so 12 times the volume of one sphere equals the volume of the cylinder. The cylinder has a radius of 2 cm and a height of 45 cm. Setting pi times 4 times 45 equal to 5 times 4/3 times pi times 27, the volume of the cylinder is 180 pi and the volume of each sphere is 36 pi. Dividing 180 pi by 36 pi results in 5 spheres.

Keep practicing — related questions