Question

Can you dearly PLEASE help me with this problem?
I know it's not 2:1.
@jdoe0001

Answer 1

did u find the volumes of both hats?

Answer 2

You do not need to find the volumes - the 2 shapes are similar.

diameter is given in m
area is measured in m^2
volume is measured in m^3

If you change the diameter by a given factor (e.g. 2:1) tyhen the volume changes by that factor^3

Answer 3

I used this formula, v=(4/3)πr² , and got 4 ; therefore, I thought it was 4:1 .

I was given this formula as well , \[r _{1}=\frac{ 18 }{ 2 }=9 inch,r _{2}=\frac{ 9 }{ 2 } inch \]
\[\frac{ V _{1} }{ V _{2} }=\frac{ \frac{ 1 }{ 3 } \pi r _{1}^3}{ \frac{ 1 }{ 3 }\pi r _{2} ^3}=\frac{ r _{1} ^3}{ r _{2} ^3} \]
\[\frac{ V _{1} }{ V _{2} }=\frac{ 9^3 }{ \left( \frac{ 9 }{ 2 } \right)^3 }=\frac{ 9^3 }{ 9^3 }\times2^3=\frac{ 8 }{ 1 } \]

\[V _{1}:V _{2}=8:1 \]

One person got 4 and the other 8:1 - so I'm confused!!!!!!!!!
@jdoe0001

Answer 4

your first formula is for a sphere. (except it shpuld be ^3 NOT ^2)

However - what I said above is true fro any similar figures. The volume is proportional to the linear dimension^3

Answer 5

Meaning, the 2nd equation I showed is correct?
May you please work this problem out with me? :/

Answer 6

I can't right now - not time.

Your 2nd equation is not correct - it doesn't include h - height of cone

But the answer is correct 'cos you have raised the radius to power 3

Answer 7

The answer is 8:1 ?

Answer 8

the diameter is only 1 unit

a volume involves 3 units
as opposed to an area that involves 2 units
so
\(\bf \cfrac{single\ unit}{single\ unit}=\cfrac{(single\ unit)^2}{(single\ unit)^2}=\cfrac{(single\ unit)^3}{(single\ unit)^3}\)

so in this case we have single units and triple ones... .thus \(\bf \cfrac{18}{\)

Answer 9

hmmm got a missing something there thus \(\bf \cfrac{18}{9}=\cfrac{18^3}{9^3}\implies \cfrac{2}{1}=\cfrac{2^3}{1^3}\)

Answer 10

that's the ratio correspondence

Answer 11

It would be 8:1 then.

Answer 12

yeap

Answer 13

That's my final answer? No more steps?

Answer 14

say for example if you were asked for the "area" ratio, that is 2 units thus that'd be \(\bf \cfrac{18}{9}=\cfrac{18^2}{9^2}\implies \cfrac{2}{1}=\cfrac{2^2}{1^2}\)

nope... that's all :)

Answer 15

Ah the area ratio is 4:1 ,
but what they're asking for is 8:1 , correct?

Answer 16

yeap they're asking on the "volume" ratio... which uses 3 units... thus yes.. is 8:1 or \(\bf 2^3:1^3\)

Answer 17

Thank you, thank you, thank you oohhh soooo much!!!! :DDD