Find the length of the base of a square pyramid if the volume is 576 cubic inches and has a height of 3 inches.
4 inches
8 inches
16 inches
24 inches

- anonymous

- katieb

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- Jack1

Volume of a pyramid = ( Length x Width x Height ) / 3
if the base is a square:
Length = width
so
Volume of a pyramid = ( Length x Length x Height ) / 3
\(\Large V = \frac{L \times L \times H}3\)
if you have the volume and the height... can you solve this for Length?

- anonymous

would the length be 576 and the height 3?

- Jack1

no, V = 576 and h = 3

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## More answers

- anonymous

oh ok sorry um.. im just wondering idk what length would be because i only have volume and height

- Jack1

sók... yep, we're trying to solve the length
if u plug the values for volume and height into the above equation... you should be left with L^2 = ... a number

- anonymous

ok 576/3 would be 192 right ??

- Jack1

\(\Large V = \frac{L \times L \times H}3\)
\(\Large 576 = \frac{L \times L \times 3}3\)
\(\Large 576 = \frac{L \times L \times \color{red}{3}} {\color{red}{3}}\)
\(\Large 576 = L \times L \)
\(\Large 576 = L^2 \)
\(\Large \sqrt{576} = \sqrt{L^2} \)
\(\Large \sqrt{576} = L \)

- Jack1

sorry does this make it clearer tho?

- anonymous

a little bit im still kinda confused bu ti some what understand

- Jack1

##### 1 Attachment

- Jack1

does the picture help?
where abouts are you getting stuck and I'll try to explain it better

- anonymous

i was just confused at the part of where we had to find the length. but that chart u showed does help a little

- Jack1

cools... so how'd u go at solving, did u get an answer for L = ...?

- anonymous

no i was still figuring it out

- anonymous

@Jack1 i dont understand what to next in the equation i keep getting confused

- Jack1

ok, well lets back it up, and you tell me which step ur having trouble with and we'll go through it together
so just say yes or no after each step, and well either keep going or explain more
so
1.
\(\Large V = \frac{L \times W \times H}3\)
2.
"base of a square pyramid"... so from question, we know it's a square pyramid
so the base is a square
Length = Width
new equation:
\(\Large V = \frac{L \times L \times H}3\)
all cool so far?

- anonymous

got it (:

- Jack1

nice
3.
from the question again:
"Find the length .... if the volume is 576 cubic inches and has a height of 3 inches. "
so find L
if V = 576
and h = 3
put the values of V and H into our equation
new equation:
\(\Large V = \frac{L \times L \times H}3\)
\(\Large 576 = \frac{L \times L \times 3}3\)
still with me?

- anonymous

sorry i was away from my computer but i understand still (:

- Jack1

all good
4.
there's a 3 top and bottom in the fraction, so it's times 3 and then divide by 3... so they cancel eachother out
\(\Large 576 = \frac{L \times L \times \color{red}{3}} {\color{red}{3}}\)
\(\Large 576 = \frac{L \times L \times 1} 1\)
\(\Large 576 = L \times L \)
\(\Large 576 = L^2 \)
all cool still?

- anonymous

ohhh ok i understand thats were i was confused before (:

- Jack1

got it then, sweet!
so are you ok to solve from here?

- anonymous

yea i think so um.. for the last where it say 576=L/2 would then be 576= 2x2?

- Jack1

no, that's L squared, so 576 = L x L
so if you take the square root of both sides
you're left with :
____ (number?) = L

- anonymous

oooh ok im sorry i feel like a dork now the 24=L correct (:

- Jack1

yep, perfect! ;)

- Jack1

and only dorks use the word dork :P

- anonymous

lol thanks ^w^ you dont mind helping me with a few more questions do you ??

- Jack1

sure there's a lot of LaTex in this post tho, so maybe open a new one so it's faster?

- anonymous

oh ok (:

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