A cone is inscribed in a regular square pyramid. If the pyramid has a base edge of 6" and a slant height of 9", find the volume of the cone.

V = (1/3) hpir²

ok, so inscribed

therefor the edge length is the diameter of the cone (the base is on bottom)

so then d=6

d/2=r

6/2=3=r

height

we need pythagoran theorem to find this

if we look at one side and draw the height then we get a right triangle with height is one leg

3 is another

and 9 is hyptonuse

a²+b²=c²

3²+h²=9²

9+h²=81

h²=72

h=6√2

h=6√2

r=3

V = (1/3) (6√2) (pi) (3²)

V=18pi√2 cubic feet

According to my calculations, the answer is 25.47 in^3.