SOLUTION: I have a couple of problems that I am trying to help my daughter to understand but I admit it's been years and I can't remember how to do them so I am going to submit them one at a

Question 140542: I have a couple of problems that I am trying to help my daughter to understand but I admit it's been years and I can't remember how to do them so I am going to submit them one at a time. I hope someone can help me help her. Here's the question. A cube has a volume of 33 cubic ,illimeters. 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? Hope someone can help!! Thanks, Jennifer
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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?
:
I'm going to use ^(1/3) for cube-root here
:
Let x = original side of the cube
:
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)
;
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?
:
Let a = scale factor
(ax)^3 = 891
ax = 891^(1/3); find the cube root of both sides
a = ; divide both sides by x
:
Substitute 33^1/3 for x:
a = =
:
a = 27^(1/3); divided 891 by 33
:
find the cube root of 27
a = 3 is the scale factor
:
:
You can check this on a calc: Enter: (3(33^(1/3)))^3 = 891
:
There is probably an easier way to do this, I just can't seem to come up with it tonight.
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