Question

What is the height of a square pyramid of base edge $12cm$ and slant height $10cm$? Find its volume.

Answer 1

For a square pyramid
Base edge $=s=12cm$
Slant height $=l=10cm$
Since the base of the pyramid is square,
Therefore, $a=\frac{diagonal}{2}$
Diagonal of square of base $12\sqrt{2}cm$
$a=6\sqrt{2}cm$
$h=\sqrt{{10}^2-a^2}=\sqrt{{10}^2-{6\sqrt{2}}^2}=\sqrt{100-72}=\sqrt{18}=3\sqrt{2}cm$
Volume$=\frac{1}{3}{s}^{2}h=\frac{1}{3}\times 18\times 8=144\sqrt{2}{cm}^3$