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Question 1199755: Two identical spheres of diameter 6 cm have the same total volume as
a) one sphere with diameter 12 cm
b) four identical spheres each with diameter 3 cm
c) eight identical spheres each with diameter 4 cm
d) sixteen identical spheres each with diameter 3 cm
e) thirty-two identical spheres each with diameter 2 cm
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
The volume is proportional to the cube of the diameter. So for the total volume to stay the same, you can...
(1) double (multiply by 2) the diameter and divide the number of spheres by 2^3=8
(2) divide the diameter by 2 and multiply the number of spheres by 2^3=8
or, in general,
(3) divide the diameter by a factor x and multiply the number of spheres by x^3
Option (2) above gives you a diameter of 6/2 = 3 cm and 2(2^3) = 2(8) = 16 spheres, which is answer choice d.
ANSWER: d) 16 spheres each with diameter 3cm
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