How do you find the volume of a square pyramid with height 12 cm and slant height 15 cm?

Question

10203 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-25T09:51:19

#color(blue)(1296cm^3)#

enter image source here
The volume of a square pyramid is given by:

#V=1/3a^2h#

Where #bba# is the side of a square and #bbh# is the height of the pyramid.

Looking at the diagram. We know the slant height and the height, but we need the length of the base side.

Using Pythagoras' theorem:

#15^2=12^2+(1/2a)^2#

#15^2=12^2+1/4a^2#

#81=1/4a^2#

#a^2=324#

#a=sqrt(324)=18#

Volume of pyramid:

#V=1/3(18)^2(12)=1296 \ \ \cm^3#