Question 140542
A cube has a volume of 33 cubic, millimeters. All 3 dimensions of the cube changed by the same scale factor so that the volume of the new cube is 891 cubic millimeters. By what scale factor did each dimension change?
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I'm going to use  ^(1/3) for cube-root here
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Let x = original side of the cube
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It says:"A cube has a volume of 33 cubic, millimeters."
x^3 = 33
find the cube root of both sides:
x = 33^(1/3)
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 All 3 dimensions of the cube changed by the same scale factor so that the volume of the new cube is 891 cubic millimeters. By what scale factor did each dimension change?
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Let a = scale factor
(ax)^3 = 891
ax = 891^(1/3); find the cube root of both sides
a = {{{891^(1/3)/x}}}; divide both sides by x
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Substitute 33^1/3 for x:
a = {{{891^(1/3)/33^(1/3)}}} = {{{(891/33)^(1/3)}}}
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a = 27^(1/3); divided 891 by 33
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find the cube root of 27
a = 3 is the scale factor
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You can check this on a calc: Enter: (3(33^(1/3)))^3 = 891
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There is probably an easier way to do this, I just can't seem to come up with it tonight.