How is the area of a circle calculated when determining total force exerted on a piston?

To calculate the area of a circle, which is essential for determining the total force exerted on a piston, the formula used is based on the diameter of the circle. The correct formula expressed as Area = D x D x 0.7854 is accurate because it directly relates to the geometry of the circle.

Here’s how it works: The area (A) of a circle can be computed using the formula (A = πR^2). Since the diameter (D) is twice the radius (R) (i.e., (D = 2R)), if we solve for (R) from the diameter, we have (R = D/2). Substituting this into the area formula gives:

[

A = π \left(\frac{D}{2}\right)^2 = π \cdot \left(\frac{D^2}{4}\right) = \frac{πD^2}{4}

]

Since (π) is approximately 3.1416, dividing this by 4 gives approximately 0.7854, leading to the area formula rewriting as (Area = D^2 x 0.7854).

This understanding