Latest 3i-Infotech Aptitude Question SOLUTION: 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)

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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

Asked In 3i-Infotech sawan kumar (12 years ago)

Solved vigneshwari Read Solution (2)

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Read Solution (2) :

vigneshwari  (11 years ago)

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

Is this solution Helpfull? Yes (14) | No (2)  

praveen  (7 years ago)

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

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