Question

A square pyramid has a base edge of 2 inches and a slant height of 5 in. Find it’s volume

Answer 1

Volume of the pyramid is V =  (Bh)/3  where B is the base area of the pyramid and h is the height to the pyramid.

B = 2(2) = 4in²
To find h, we need to use the Pythagorean theorem.  The height of the pyramid is actually an altitude that drops straight down from the vertex of the pyramid perpendicular to the Base hitting the Base in the center.  Therefore, the distance from where the altitude hits the Base and the edge of the Base is equal to 1. We are given the slant height as 5 inches so we can now use the theorem to find the height of the pyramid.
h² + 1² = 5²
h² = 5² - 1²
h² = 25 - 1
h² = 24
$h = \sqrt{24}$
$h=2 \sqrt{6}$
Now we can find the Volume:
V= (Bh)/3
$V= \frac{[4(2 \sqrt{6} )]}{3}$ 
$V = \frac{8}{3} \sqrt{6}$
This is about 6.5 in³ of volume