Question

The surface areas of two similar figures are given. The volume of the larger figure is given. Find the volume of the smaller figure.

Answer 1

what is figure?
is it sphere?

Answer 2

it was not specified

Answer 3

use the same idea as the last problem.
first find the ratio of their "sides" (i.e. the square root of the ratio of their surface areas)

then cube that ratio to get the ratio of volumes.

Answer 4

doesnt this only work if it happens to be a cuve tho

Answer 5

\[\frac{ \sqrt52 }{ \sqrt192 }\]

Answer 6

@dan815 amazingly it works for any *similar volumes*

Answer 7

ya i know it doesnt work for cube

Answer 8

now i am confused

Answer 9

for a cube of side=1, its surface area is 6
cube side= 2, its surface area is 24
ratio of surface areas is 6/24 = ¼
square root gives us ½ ( the ratio of their lengths)
cube ½ to get ⅛ ratio of their volumes

Answer 10

@highschoolmom2010 you are on the right track...

Answer 11

Sorry, dan was wrong, not highschoolmom

Answer 12

oh ok

Answer 13

except you want the ratio of surface areas... in other words 52/208
that you take the square root of.

Answer 14

oh ok

Answer 15

\[\frac{ \sqrt52 }{\sqrt 208 }=\frac{ 1 }{ 2 }\]

Answer 16

now cube that ratio to find the ratio of their volumes.

Answer 17

\[\frac{ 1^3 }{ 2^3 }=\frac{ 1 }{ 27 }\]

Answer 18

it works for spheres too but, its hard to see, how can it work for any sorface and volume possible

Answer 19

\[\frac{ x }{ 52 }=\frac{ 1 }{ 27 }\]

Answer 20

is it because technically any volume can be broken down into a sum of little cubes

Answer 21

½ cubed is not 1/27
½ * ½ * ½ = ?

Answer 22

oh ok

Answer 23

\[1/8\]

Answer 24

yes, now set up your ratio of volumes

Answer 25

\[\frac{ x }{ 52 }*52=\frac{ 1 }{ 8 }*52\]

Answer 26

where did you get 52 ?

Answer 27

for the original question

Answer 28

wait i see

Answer 29

\[\frac{ x }{ 192 }*192=\frac{ 1 }{ 8 }*192\]

Answer 30

much better!

Answer 31

X=24

Answer 32

looks good.

Answer 33

hooray thanks @phi @dan815

Answer 34

suer

Answer 35

=]