Hi, I've been working on a problem which I thought would be quite easy - but the answer I got was incorrect. Can someone please help me?
In a certain regular square pyramid, all of the edges have length 12. Find the volume of the pyramid.
Thank you so much!!!
the formula for the volume of a pyramid is length*width*height/3. We know the length and the width but we don't know the height. Since we know this is a regular pyramid, and we know all edges have the length of twelve, we can draw a triangle with the information we know
height^2 + (1/2*length)^2 = k^2(where k is the length from any corner to the tip of the pyramid.) know we plug in the information we know.
height^2 + 36 = 144
height = 6 root 3.
so then we plug in those values in to the formula for a pyramid and get 12*12*6 root 3 /3
=48*6(sqrt108) = 1728*sqrt(3)
1) Diagonal of a square d = sqrt( 122 + 122 ) = 16.97056275 d/2 = 8.485281374
2) Height of a pyramid h = sqrt( 122 - 8.4852813742 ) = 8.485281374 ()
3) Volume of the pyramid V = lwh/3 = (12*12*8.485281374) /3 = 407.293506 u3
" height = 6 root 3 " this is slant height
You need the altitude (height) of the pyramid to calculate the volume.
I'll use your slant height to find the height of the pyramid.
h = sqrt[( 6*√3)2 - 62 ] = sqrt( 108 - 36 ) = 8.485281374
We can use slant height this way: V = [ 12 * 12 + (6√3) ] / √13.5 = 407.293506 u3