For Josh's science project he is filling a mountain with fake lava liquid. The mountain he created was in the shape of a square pyramid with a base length of 12 inches. If 432 square inches of liquid fits into the pyramid, what is the pyramids height ???

Question

theeric · Answer

Hi! Do you have any idea where to start?

anonymous · Answer

nope

theeric · Answer

Alright! Well here's the thing:|dw:1374963754287:dw|You know the base length, and how much the volume is.

theeric · Answer

|dw:1374963857904:dw|

anonymous · Answer

volume is 432 ?

theeric · Answer

The formula for the volume of a square pyramid is $V=\frac{1}{3}b^2\ h$, as I found online. http://formulas.tutorvista.com/math/volume-of-a-square-pyramid-formula.html Yep, volume is 432, and it should be in cubic inches, not square inches.

theeric · Answer

$b$ is the base length
$h$ is the height
$V$ is the volume.
So you solve for $h$! Can you take care of the rest, then? I'll hang here, to double-check your answer and answer any questions you might have.

anonymous · Answer

so.. 432=1/3(12)^2

anonymous · Answer

what would i do next multiply 1/3 and 12^2

theeric · Answer

$$432\ [in^3]=\frac{1}{3}(12\ [in])^2\ h$$

theeric · Answer

You just forgot the $h$, is all. And that's what you need to solve for.

How are you with algebra?

anonymous · Answer

im good i guess

theeric · Answer

Alright, so you have$$V=\frac{1}{3}b^2\ h$$What first, to get at $h$ alone?

anonymous · Answer

well to undo the division you multiply

theeric · Answer

Alright! If you want to tell me what to do, I'll change the formula for you. So multiply by $3$, I think you're saying.
$$\frac{V}{3}=\frac{1\times\cancel 3}{\cancel 3}b^2\ h=b^2\ h$$$$\qquad\Downarrow$$$$\frac{V}{3}=b^2\ h$$Now?

anonymous · Answer

then you can go ahead and do 12^2

theeric · Answer

Okay!$$\frac{V}{3}=b^2\ h=(12)^2\ h=144\ h$$$$\qquad\Downarrow$$$$\frac{V}{3}=144\ h$$

anonymous · Answer

wait 432/3 is 144 so 144=144 is 1 ?

theeric · Answer

Yeah, $1=h$! I guess that's your answer!

theeric · Answer

|dw:1374965054826:dw|$\huge\color{blue}{\large\ \ o\ o\ \\smile}$

anonymous · Answer

let mee see if its right

theeric · Answer

Okay.

anonymous · Answer

its not ? :( the answer isnt 1

theeric · Answer

Are there different options for different units?

theeric · Answer

Or are you required to put in the units?

theeric · Answer

Oh gosh, I did it wrong, sorry.

theeric · Answer

That was my fault.
$$3\times V=144\ h$$

anonymous · Answer

ok

theeric · Answer

Yielding $9=h$. I'm sorry.

anonymous · Answer

and what unit do i put

anonymous · Answer

square inches