Final answer:
The correct function for the length of the base edge of a right square pyramid with a height of 8 inches as a function of its volume is C. a(v) = square root of (3v/8).
Step-by-step explanation:
To find the function that gives the length of the base edge, a(v), of a right square pyramid as a function of its volume, v, with a given height of 8 inches, let's start with the formula for the volume of a pyramid, V = (1/3)Abh, where V is the volume, Ab is the base area, and h is the height. For a square base, Ab = a2, so the volume formula becomes V = (1/3)a2h. Given that h = 8 inches, we can rewrite this as v = (1/3)a2(8) or v = (8/3)a2. To solve for a, we need to 'undo' the square on a by taking the square root and rearrange the equation to isolate a: a(v) = √(3v/8).
Therefore, the correct answer is C. a(v) = √(3v/8).