A cylinder is 6 cms in diameter and 6 cms in height. If spheres of the same size are made from the material obtained, what is the diameter of each sphere?

(a) 5 cms (b) 2 cms (c) 3 cms (d) 4 cms

• since the sphere is made out of the cylinder material their volume will be same
  
  volume of cylinder = pi * 3^2 * 6
  volume of one sphere = 4/3 * pi * r ^3 (where r is radius of sphere)
  
  so if there are N such sphere's
  equating the volumes,
  
  pi*r^2*h = N*(4/3)*pi*R^3
  
  N is the number of spheres,
  
  substituting the, r and h
  9*6 = N*(4/3)*(D/2)^3
  
  D is the diameter of a sphere,
  N = (9*6*3*8)/(4*D^3)
  N = 324/D^3
  
  now substitute the given answers for D and find the values for N, since a N has to be an integer only value fit for D is 3,
  
  answer is C
• 11 years agoHelpfull: Yes(14) No(2)
• volume of cylinder(V) = pi * r^2 * h where r is radius and h is height
  V = (3.14) * 3^2 * 6 = 169.56 cm^3
  note using pi = 3.14
  now we divide the volume by 12, 169.56 / 12 = 14.13 cm^3
  each of the 12 spheres has a volume of 14.13 cm^3
  volume of a sphere is (4/3)*pi*r^3
  14.13 = (4/3) * (3.14) * r^3
  
  
  multiply both sides of = by 3
  42.39 = 12.56 * r^3
  divide both sides of = by 12.56
  r^3 = 3.367834395
  r = 1.498937677 approx 1.5
  diameter = 2 * 1.5 = 3 cm
  the answer is b
• 7 years agoHelpfull: Yes(0) No(3)