A cylinder is 6 cms in diameter and 6 cms in height.
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?
Answer/Solution
3 cms
Steps/Work
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:C
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:C