Question

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

Answer 1

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?

Answer 2

i dont know

Answer 3

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.

Answer 4

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.

Answer 5

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

Answer 6

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

Answer 7

ok so 2*208pi

Answer 8

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.

Answer 9

So we would multiply 208pi by 4.

Answer 10

208*pi*4=2612.48

Answer 11

?

Answer 12

Yes

Answer 13

so that would be the surface area?

Answer 14

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

Answer 15

Yes that is your surface area.

Answer 16

320*pi*8=8038.4

Answer 17

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

Answer 18

Seems good to me.

Answer 19

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

Answer 20

Hang on.

Answer 21

ok

Answer 22

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

Answer 23

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.

Answer 24

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.

Answer 25

so 96*pi*

Answer 26

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)

Answer 27

so 535.89cm squared

Answer 28

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

Answer 29

4/3 cubed would be

Answer 30

well 4 cubed over 3 cubed

Answer 31

64/27

Answer 32

Yes :)

Answer 33

so then for volume i get 714.52cm cubed

Answer 34

Yup