Question

A pyramid has a square base with sides of length s. The height of the pyramid is eqaul to 1/2 of the length of a side base. Which formula represents the volume of a pyramid?
A) V=1/12s^2
B) V=1/6s^3
C) V=1/3s^3
D) V=3s^3
E) V=6s^3

Answer 1

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