# Geometry

posted by on .

If eacj dimension of a box is quadrupled, how are the surface area and the volume affected?

• Geometry - ,

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

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

here is the formula
TA = 2Lw + 2Lh + 2wh

• Geometry - ,

which one is length width height

• Geometry - ,

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 - ,

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 - ,

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.