Posted by crystal on .
If eacj dimension of a box is quadrupled, how are the surface area and the volume affected?

Geometry 
helper,
I'll do volume to show you
V = L*w*h
1st example, L = 2, w = 3, h = 4
V = 2*3*4
V = 24
Quadruple each dimension,
L = 2*4 = 8, w = 3*4 = 12, h = 4*4 = 16
V = 8*12*16
V = 1536
So, the volume went from 24 to 1536
1536/24 = 64 so 24*64 = 1536
So, if you quadruple the dimensions, the volume is increased 64 times
Follow this for the Area
here is the formula
TA = 2Lw + 2Lh + 2wh 
Geometry 
crystal,
which one is length width height

Geometry 
helper,
I don't understand what you are asking
use this formula
TA = 2Lw + 2Lh + 2wh
use these dimensions
1st use, L = 2, w = 3, h = 4
then quadruple the dimensions to compare how the area changed
2nd use L = 8, w = 12, h = 16 (I quadrupled the dimensions for you)
you can use any dimensions you want, I just gave you dimensions for example 
Geometry 
Reiny,
original:
length = L
width = W
height = H
V = LWH
SA = 2(LW + LH + WH)
new one:
length = 4L
width = 4W
height = 4H
volume = (4L)(4W)(4H)
= 64 LWH
so the volume is 64 times as large, helper had that also.
SA = 2(16LW + 16LH + 16WH)
= 32(LW + LH + WH)
so the surface area is 32 times as large. 
Geometry 
helper,
I can't believe I didn't think to do it your way!!!
so much easier to do AND understand
that's why you are the tutor
thank you
I've learned so much from your posts! I wish I had you to ask questions when I was taking math.