Posted by StephanieNZ on Sunday, March 21, 2010 at 12:58am.
You were correct,
when you cut the radius in half, the volume will be 1/8 of the original.
When you triple the radius, the new volume will be 27 times that of the original.
Look at what happens when we substitute the new radius for r
sub in 3r for the radius
V = (4/3)π(3r)^3
= (4/3)π)(27)r^3
= 27 * (4/3)πr^3
Notice that the volume changes by the cube of the scaling factor,
taking 1/2 ----> (1/2)^3 = 1/8
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