Question

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, in cubic inches?

Answer 1

$\text{Given that the height of the right square pyramid is 8 inches}\\ \text{we need to find the length of the base edge of the right square pyramid a(v)}\\ \\ \text{we know that the volume of a right square pyramid with base edge a and }\\ \text{height h is given by}\\ \\ V=\frac{1}{3}a^2 h\\ \\ \text{so using this formula, we get}$

$V=\frac{1}{3}\times a^2 \times 8\\ \\ \Rightarrow V=\frac{8}{3}a^2\\ \\ \text{multiply both sides by }\frac{3}{8}, \text{ we get}\\ \\ a^2=\frac{3V}{8}\\ \\ \text{take square root both sides to get}\\ \\ a=\sqrt{\frac{3}{8}V}\\ \\ \text{Hence the length of the base edge is: }a(V)=\sqrt{\frac{3}{8}V}$

Answer 2

what r the answers to chose from