What is the surface area of the box if it is scaled up by a factor of 10?

Question

anonymous · Answer

The surface area of the box is 3246.54x (exponent 3).

anonymous · Answer

How do you figure this out?

anonymous · Answer

@Hero

e.mccormick · Answer

How can a surface area be cubic?

anonymous · Answer

i dont know lol i didnt do my work by hand

anonymous · Answer

1. List the dimensions of your box. Be sure to include the units (in, cm, ft., etc.).
2. Describe the shape of the cross section when the box is cut parallel to the base.
3. What is the surface area of the box?
4. What is the surface area of the box if it is scaled up by a factor of 10?
5. What is the volume of the box?
6. What is the volume of the box if it is scaled down by a factor of ½?      

This is what i got so far to step 2 ....
Notebook (Rectangular Prism)
Height – 10  ½ inches 
Width – 0.0984252 inches 
Length – 8  1/8 inches

The shape has 4 parallel sides, it is a rectangular prism. The height would be 8 1/4 the width would be ¼ and the length would be 5 ½.

e.mccormick · Answer

Lines are single dimensional lengths, so go ip by linear values.
Area is a square value, so they go up exponentially by 2.
Volume is a cubic value, so it goes up exponentially by 3.

1 by 1 by 1 box to a 2 by 2 by 2 box to a 3 by 3 by 3 box...

Lines: 1, 2, 3.
Surface of one side: 1, 4, 9
Volume: 1, 8, 27

Notice a trend?

anonymous · Answer

Yes i do

e.mccormick · Answer

That is a narrow box!

anonymous · Answer

still a box sorta
Its still a rectangular prism

e.mccormick · Answer

Yes.  K, gonna check some math...

anonymous · Answer

ok

e.mccormick · Answer

How did you get that surface area?

anonymous · Answer

i did sa = 2 (wl + hl + hw)

e.mccormick · Answer

2(0.79970475 + 85.3125 + 1.0334646) = 174.2913387

e.mccormick · Answer

Now, if all the sides are up-scaled by 10, it becomes:

sa = 2 (10w 10l + 10h 10l + 10h 10w)
sa = 2 (100wl + 100hl + 100hw)
sa = 2*100 (wl + hl + hw)

So when you have the correct numbers, multiply by 100 to make something 10 times as long to see the new surface area.  And 10^2=100... which is how it relates to what I was showing earlier.

For the volume one, look at $\left(\dfrac{1}{2}\right)^3$ for what to multiply by.  Same principal applies.  Half of each side, but cubed for area.