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 pyramid's height?

Question

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 pyramid's height?

mathstudent55 · Answer

For a pyramid, the volume is
$ V = \dfrac{1}{3}Bh $
where B = area of the base.

For a square, the area is
$A = s^2 $
where s = length of the side of the square.

mathstudent55 · Answer

The amount 432 is in cubic inches or square inches?

anonymous · Answer

square inches

anonymous · Answer

@mathstudent55 would the hieght be 36

mathstudent55 · Answer

How can you fill something with an amount in square inches? Square inches is a unit of area. If you're filling a pyramid, you need an amount in cubic inches, a unit of volume.

mathstudent55 · Answer

Is the pyramid being filled with fake lava or covered with fake lava?

anonymous · Answer

filled

mathstudent55 · Answer

Is 432 supposed to be in cubic inches and is the volume of the pyramid, or is 432 supposed to be in square inches an is the surface area of the pyramid?

mathstudent55 · Answer

If the pyramid will be filled, then it has to be 432 cubic inches, not 432 square inches, of fake lava.

mathstudent55 · Answer

$V = Bh $

$ 432 ~in.^3 = 12^2 ~in.^2 h$

$h = \dfrac{432~in.^3}{144 ~in.^2} = h $

$h = 3 ~in. $

anonymous · Answer

0hk thanks for explainig cause i would have put sq inches

mathstudent55 · Answer

wlcm