# Geometry

posted by .

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.

## Similar Questions

1. ### Calculus

a rectangular box of given volume is to be "a" times long as it is wide. find the dimension for which it has the least total surface area ?
2. ### MATH-Stuck

For each of the following, the Surface Area is given. Calculate the missing dimension. This is a rectangular prism with the width missing. The height seems to be 20 cm. The length I guess is 34 cm, and the Surface Area is 6020cm square. …
3. ### Math

Check my answer please? Yuri is wrapping presents. The first box measures 9 inches by 12 inches by 2 inches. He has a second box with dimensions that are each half of the length of the first box. How does the surface area of the second
4. ### math

a smaller box has dimension that half the measurements of the orignal . find the ratio of the surface area of the orginal box to the surface area of the smaller box
5. ### calcules

we want to construct a box with a square base and no top. the volume of the box will be 8 cm^3 what are the dimension of the minimize the surface area .
6. ### math

The dimension of a closed cuboid box are in the ratio 5:4:3 if the total surface area is 0.94m^2,find the dimension of the box.
7. ### Intermediate Algebra

A parcel delivery service has contracted you to design an open box with square base length x cm and height y cm has a volume of 3600 cubic cm. Find the total surface area in terms of x and y. Also determine the dimension for minimum …
8. ### math

a manufacturer wants to design an open box that has a square base and a surface area of 48sq units what dimension will produce a box with a maximum volume?
9. ### Geometry,Math

Is my data correct? For package design I will use a cylinder. The Equation for the surface area of a cylinder is A = 2 π r h + 2 π r² . The equation for the volume of a cylinder is V = π r² h. I have chosen a cylinder
10. ### math

The dimension of a rectangular metal box are 3 cm,5cm and 8cm.if the first two dimensions are increased by the same number of centimeters, while the third dimension remains the same, the new volume is 34 cubic cetimeters more than …

More Similar Questions