Question

A pyramid has a square base with sides of length s. The height of the pyramid is equal to 1/2 of the length of a side on the base. Which formula represents the volume of the pyramid?

Answer 1

$A\ volume\ of\ a\ square\ pyramid:\\\\V=\dfrac{1}{3}a^2H\\\\a-length\ of\ a\ side\ of\ a\ base\\H-a\ height\ of\ a\ pyramid\\-------------------\\a=s;\ H=\dfrac{1}{2}s\\\\subtitute\\\\V=\dfrac{1}{3}s^2\cdot\dfrac{1}{2}s=\dfrac{1}{6}s^3\\\\\boxed{V=\frac{1}{6}s^3}$

Answer 2

The volume of the pyramid is a third of the volume of the prism which has the same base area and height as the pyramid. That is,
                           V = b²h / 3
Substituting the variables given,
                          V = (s²)(0.5s) / 3
Simplifying,
                          V = s³/6