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

Answer:

Explanation:

The formula of a volume of a square pyramid:

a - base edge

h - height of a pyramid

We have H = 8in.

Substitute and solve for a:

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Explanation:

Answer 2

`\large\boxed{a(V)=\sqrt{(3V)/(8)}}`

Explanation:

The formula of a volume of a square pyramid:

`V=(1)/(3)a^2h`

a - base edge

h - height of a pyramid

We have H = 8in.

Substitute and solve for a:

`(1)/(3)a^2(8)=V\\\\(8)/(3)a^2=V\qquad\text{multiply both sides by}\ (3)/(8)\\\\(3\!\!\!\!\diagup^1)/(8\!\!\!\!\diagup_1)\cdot(8\!\!\!\!\diagup^1)/(3\!\!\!\!\diagup_1)a^2=(3)/(8)V\\\\a^2=(3V)/(8)\Rightarrow a=\sqrt{(3V)/(8)}`