anonymous
  • anonymous
The solid is similar to a larger solid with the given scale factor. find the surface area and volume of the larger solid
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
Ok so basically it's asking what dimensions you will have after you scale it. So the first one is supposed to be 2 times as large as your original. You are given surface area of your original shape and the volume of your original shape. What do you have to do to scale the shape properly?
anonymous
  • anonymous
i dont know

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anonymous
  • anonymous
Well lets think about it. Lets say you have a flat square that is 2 foot length by 2 foot width. This square has a surface area of 4 feet squared.
anonymous
  • anonymous
Now if you increased your dimensions by 2, you would have a 4 feet x 4 feet square. This would give us 16 feet squared as our surface area. If you see, 16 is simply 4 squared.
anonymous
  • anonymous
By increased dimensions i mean multiplied by 2 to double it's dimensions
anonymous
  • anonymous
So since our length and width was doubled, our original area was squared to give us our new surface area.
anonymous
  • anonymous
ok so 2*208pi
anonymous
  • anonymous
Ok forget what I said. If we are doubling our dimensions we need to actually multiply our surface area that we are given by 4. Sorry about that it's been a long time since I've done this stuff.
anonymous
  • anonymous
So we would multiply 208pi by 4.
anonymous
  • anonymous
208*pi*4=2612.48
anonymous
  • anonymous
?
anonymous
  • anonymous
Yes
anonymous
  • anonymous
so that would be the surface area?
anonymous
  • anonymous
And for the Volume we need to multiply by a factor of eight since we are scaling by 2.
anonymous
  • anonymous
Yes that is your surface area.
anonymous
  • anonymous
320*pi*8=8038.4
anonymous
  • anonymous
The units of surface area will be inches squared in this case, and Volume will be inches cubed.
anonymous
  • anonymous
Seems good to me.
anonymous
  • anonymous
can we do the circle of triangle cuz i think i can do the rectangle
anonymous
  • anonymous
Hang on.
anonymous
  • anonymous
ok
anonymous
  • anonymous
Ok the cone is a 3:4 scale, which means we are enlarging the object by a factor of 1/3
anonymous
  • anonymous
Actually it's a factor of 4/3. Now since your scale factor is 4/3, you will square 4/3 for the number you need to multiply your original area to find your new area.
anonymous
  • anonymous
And for your volume, you need to cube 4/3 to find your number that you need to multiply your original volume by to get your new volume.
anonymous
  • anonymous
so 96*pi*
anonymous
  • anonymous
it would be 96pi times (4/3) squared. To square 4/3 you just square the top and bottom. You would get 16/9. so 96pi * (16/9)
anonymous
  • anonymous
so 535.89cm squared
anonymous
  • anonymous
sure. and for the volume we cube (4/3) and multiply it by our original volume.
anonymous
  • anonymous
4/3 cubed would be
anonymous
  • anonymous
well 4 cubed over 3 cubed
anonymous
  • anonymous
64/27
anonymous
  • anonymous
Yes :)
anonymous
  • anonymous
so then for volume i get 714.52cm cubed
anonymous
  • anonymous
Yup

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