Which of the following gives the correct expression for D given the area A = 0.7854D²?

To derive the correct expression for D from the formula given for the area, A = 0.7854D², we need to isolate D in the equation.

Starting with the original equation, we want to solve for D:

1. A = 0.7854D²

2. To get D² by itself, divide both sides of the equation by 0.7854:

D² = A / 0.7854

3. Next, to solve for D, take the square root of both sides:

D = √(A / 0.7854)

This derivation confirms that the expression for D is indeed D = √(A / 0.7854), which is why this option is correct.

Calculating D in this manner is essential as it allows for determining the diameter based on a given area in contexts such as fluid mechanics and engineering, where understanding the relationship between area and diameter is fundamental to the design and analysis of various systems. The square root is crucial in transforming the relationship to solve for a linear dimension (D) from an area measurement (A).