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What is the formula for finding the height of a square pyramid who's volume is 8 cubic feet and a base length of 2 ft?

- Elise_a18

- chestercat

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- Elise_a18

- Vocaloid

good, so we have
V = (1/3)(r^2)(h)
we have V and r, and we want to find h

- Elise_a18

yep:)

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## More answers

- Vocaloid

so we re-arrange our formula to get
h = 3V/(r^2)
now plug in V and r

- Elise_a18

I'm having a heard time isolating h

- Vocaloid

ok, want me to walk you through it?

- Elise_a18

Oh! wait!

- Vocaloid

nope, this formula works for a square pyramid
a cone would be (1/3)(pi)r^2h

- Vocaloid

if r = the side length of the base, that is

- Elise_a18

Alright, let's start again. I have 2 formulas for a square pyramid
\[\frac{ 1 }{ 6 } (b^3) \] and \[\frac{ 1 }{ 3 } (b) (h)\]

- Vocaloid

hm... the first formula only works if the height is equal to the side length of the base

- Vocaloid

lets use the second formula
V = (1/3)bh where b is the area of the base and h is the height

- Elise_a18

|dw:1444411817781:dw|

- Elise_a18

Okay so the formula would be \[\frac{ 1 }{ 3 } (2) (h)\]

- Vocaloid

oh, ok, if 2 is the area of the base, then yes

- Vocaloid

V = (1/3)(2h)
now multiply both sides by to "get rid of" the 1/3

- Elise_a18

base length rather :P

- Elise_a18

- Vocaloid

wait, why "cubic feet"? that implies 3 dimensions

- Vocaloid

if the side length is 2, then the base is 4

- Elise_a18

yeah, it's a square pyramid. like in my drawing

- Elise_a18

Ohh right! I forgot that BL= S^2

- Vocaloid

right, so if b = 4 then
V = (1/3)(4)(h)
know how to isolate h now?

- Elise_a18

Yeah I did it on my white board. Would it be h= \[\frac{ 1 }{ 3 } *8\frac{ 4 }\]

- Elise_a18

oh. O-o

- Vocaloid

nope, not quite

- Elise_a18

|dw:1444412375012:dw|

- Vocaloid

we want to "get rid of" the 1/3 fraction so we multiply both sides by 3

- Elise_a18

not like this?

- Vocaloid

V = (1/3)(4)(h)
3V = 4h
with me so far?

- Elise_a18

yes. So it would be V=8 right? because the vol is already given?

- Elise_a18

OH! it's 6?

- Vocaloid

nope, remember, we want to find h

- Vocaloid

3V = 4h
now divide both sides by 4

- Elise_a18

i though we need to divide 3V by 4 to isolate h?

- Vocaloid

right

- Vocaloid

h = 6, right

- Vocaloid

didn't see your answer up there ;P

- Elise_a18

Yeay! Thank you so much! I know I'm kinda slow but I love it when I can actually understand X)

- Elise_a18

i was seeing that V is substituted by 8

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