Posted by tl on Monday, February 6, 2012 at 8:45pm.
Assume the smaller ball has a volume of 45.
Since volume is proportional to r^3, and R = 3r, the larger V is 3^3 as big as the smaller v, or 27*45 = 1215.
for the details, see below
for the smaller ball, v = kr^3 with k=4pi/3
The larger ball with radius R=3r has volume
V = kR^3 = k(3r)^3 = 27kr^3 = 27v = 27*45 = 1215
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