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

1 Answer
Apr 25, 2018

color(blue)(1296cm^3)

Explanation:

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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