Question

Help please with volume question!

Answer 1

@MagMonk Can you help?

Answer 2

Yeah I believe I can.... let me double check my work...

Answer 3

Okay thank you so much :)

Answer 4

Sure np

Answer 5

@AJ01 Do you have any idea? Because I don't know where to begin...

Answer 6

The ratio of the surface areas of two similar solids is the square of their scale factor.

Square root: (4 / 9 ) = 2/3 or 2 : 3 as the scale factor.

The cube of the scale factor is the ratio of the volumes of the two similar figures.

(2/3)^3 = x / 216

8 / 27 = x /216

x = 64 cubic inches --> volume of smaller solid

Answer 7

@campbell_st Can you clarify too? I mean it looks like it makes sense. I need to keep rereading it to understand it but...

Answer 8

9 in ---> 216
4 in---->x
x=(4*216)/9=96

Answer 9

and that becuase the are similar

Answer 10

so 96 now? I'm a bit confused now...

Answer 11

ok..so there is a few things to know...

if the ratio of the linear measurements is a:b

then the ratio of area, or surface areas is \[a^2:b^2\]

and the ratio of the volumes is \[a^3: b^3\]

so you are tole the surface areas are

4:9 when written in ratio...

so take the square root of each part the find the linear measurement ratios... or scaling factor

\[\sqrt{4}:\sqrt{9} ~~is~~ 2:3\]

Then you need to cube the linear ratios to find the ratio of the volumes

\[2^3 :3^3 ~~is~~ 8:27\]

so the ratio of the volumes is 8:27

the ratio to find the missing volume use

\[\frac{8}{27} = \frac{x}{216}~~~then~~~ x = \frac{8 \times 216}{27}\]

hope it makes sense... and all the working of @MagMonk is correct

Answer 12

Wow thank you both so much! Really helped me out :)

Answer 13

Sure no problem, glad to help ^-^

Answer 14

I have another question similar to it, if you can help me again. If it's too much for you to figure out right now, that's okay too.

Answer 15

I'm just beginning this and trying to understand, but it's a bit overwhelming.

Answer 16

just multplying (4*216)/9=96
if 9 in^2 gives 216in^3 then 4 in^2 gives x