SOLUTION: a square pyramid has base edge length 10 cm. the slant height of the pyramid is 13 cm. what is the volume of the pyramid?

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Question 965309: a square pyramid has base edge length 10 cm. the slant height of the pyramid is 13 cm. what is the volume of the pyramid?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You want the height of the pyramid so you could use volume as %281%2F3%29h%2As%5E2, where s is side length of the base and h is height of pyramid. The given slant height will help you find the pyramid height.

Let slant height be L, and h be pyramid height, and s be base edge length.
The slant height is the hypotenuse of a triangle with legs s/5 and L.

h=sqrt%28%28s%2F5%29%5E2%2BL%5E2%29

You have for this,
h=sqrt%28%2810%2F2%29%5E2%2B13%5E2%29
h=sqrt%2825%2B169%29
h=sqrt%28194%29

Your volume is %281%2F3%29sqrt%28194%2910%5E2 which you can simplify.