Which of the following functions gives the length of the base edge, a(v), of a right square pyramid that is 8 inches tall as a function of its volume, v, incubic inches?

Accepted Solution

Answer:[tex]\large\boxed{a(V)=\sqrt{\dfrac{3V}{8}}}[/tex]Step-by-step explanation:The formula of a volume of a square pyramid:[tex]V=\dfrac{1}{3}a^2h[/tex]a - base edgeh - height of a pyramidWe have H = 8in.Substitute and solve for a:[tex]\dfrac{1}{3}a^2(8)=V\\\\\dfrac{8}{3}a^2=V\qquad\text{multiply both sides by}\ \dfrac{3}{8}\\\\\dfrac{3\!\!\!\!\diagup^1}{8\!\!\!\!\diagup_1}\cdot\dfrac{8\!\!\!\!\diagup^1}{3\!\!\!\!\diagup_1}a^2=\dfrac{3}{8}V\\\\a^2=\dfrac{3V}{8}\Rightarrow a=\sqrt{\dfrac{3V}{8}}[/tex]