The solid is similar to a larger solid with the given scale factor. find the surface area and volume of the larger solid

- anonymous

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- anonymous

##### 4 Attachments

- 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

i dont know

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## More answers

- 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

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

By increased dimensions i mean multiplied by 2 to double it's dimensions

- anonymous

So since our length and width was doubled, our original area was squared to give us our new surface area.

- anonymous

ok so 2*208pi

- 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

So we would multiply 208pi by 4.

- anonymous

208*pi*4=2612.48

- anonymous

?

- anonymous

Yes

- anonymous

so that would be the surface area?

- anonymous

And for the Volume we need to multiply by a factor of eight since we are scaling by 2.

- anonymous

Yes that is your surface area.

- anonymous

320*pi*8=8038.4

- anonymous

The units of surface area will be inches squared in this case, and Volume will be inches cubed.

- anonymous

Seems good to me.

- anonymous

can we do the circle of triangle cuz i think i can do the rectangle

- anonymous

Hang on.

- anonymous

ok

- anonymous

Ok the cone is a 3:4 scale, which means we are enlarging the object by a factor of 1/3

- 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

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

so 96*pi*

- 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

so 535.89cm squared

- anonymous

sure. and for the volume we cube (4/3) and multiply it by our original volume.

- anonymous

4/3 cubed would be

- anonymous

well 4 cubed over 3 cubed

- anonymous

64/27

- anonymous

Yes :)

- anonymous

so then for volume i get 714.52cm cubed

- anonymous

Yup

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