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

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

which one is length width height

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

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.

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.

If each dimension of a box is quadrupled, it means that the length, width, and height of the box are all multiplied by 4.

To understand the effect on the surface area and volume, we need to consider the formulas for calculating them.

1. Surface Area of a box:
The surface area of a box is given by the formula: 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

If each dimension is quadrupled, the new dimensions of the box would be 4 times the original dimensions. So the new length (l') would be 4l, the new width (w') would be 4w, and the new height (h') would be 4h.

Plugging these new dimensions into the formula, we get:
New Surface Area = 2(l'w' + l'h' + w'h')
= 2(4lw + 4lh + 4wh)
= 2(4(lw + lh + wh))
= 8(lw + lh + wh)

This means that when each dimension is quadrupled, the surface area of the box is increased by a factor of 8.

2. Volume of a box:
The volume of a box is given by the formula: V = lwh.

Similar to the surface area, if each dimension is quadrupled, the new dimensions become 4 times the original dimensions. So the new volume (V') would be:
New Volume = (l')(w')(h')
= (4l)(4w)(4h)
= 64(lwh)
= 64V

This means that when each dimension of a box is quadrupled, the volume of the box is increased by a factor of 64.